Sine waves have no harmonics – as we’ll learn in future installments – sine waves are what we combine to make more and more complex wave shapes. The basic organ sound is a combination of sine waves to make a composite tone. It is the relative volumes, how loud each of the ascending harmonics are relative to each other, that makes each pipe or drawbar setup unique to our ears. Identifying the relative loudness of harmonics is going to be true throughout all musical instruments and sounds in general. The harmonic fingerprint of a trumpet is slightly different from the harmonic fingerprint of a fluegelhorn… Even when playing the same note, a subtle difference in loudness among the upper harmonics alerts our brain that each is a different instrument. Identification is assured. To recreate the timbre of a complex sound, matching the amplitude (or loudness) of the first few harmonics is critical – if you can accurately reproduce 5 harmonics the listener will begin to identify the sound with a particular sound category. The more of the harmonics you are able to match the more convincing your emulation will sound.

Whether based on tone wheels, transistors or integrated circuits, the designers of electronic organs selected the most consonant (nearest) harmonics for the front panel control. Starting with the fundamental 8′ (A110 in our example), the second harmonic is 4′ (A220), the next would be the fundamental times 3, this yields a note one octave plus a musical fifth above. Approximately, an “E” E330, called the perfect fifth. The Fundamental times 4 is the second octave above at A440. The Fundamental times 5 gives us, approximately, C#550, and times 6 gives us, approximately, E660… We say “approximately” because of Equal Temperament (the division of the octave into 12 equal parts comes into play here). Instead of the mathematics being strictly accurate, we’ve elected a scale that is convenient for all keys. By the time we get to the 7th harmonic our note is enough ‘out of tune’ to be troubling… We’ll see this up close in a future installment. The note closest to 770 cycles per second is the G at 783.99Hz.

“Equal Temperament”, for those interested, is steeped in the deeper mathematics of modern music and will remain (for now) outside the discussion here. The purpose here is to give enough background to begin programming your own sounds with some degree of confidence! Intuitively, rather than the empirical scientific method. It can be done! Let’s just say that a “perfect fifth” is only almost perfect in Equal Temperament.

At any rate the harmonic Drawbars skip the 7th harmonic and just jump to the next useful (supportive) tone, the 8th harmonic at the octave at 880. Much is written about avoiding the 7th harmonic (the seventh wave) and as we get deeper into this, you will understand and hear why. The 7th harmonic is so out of sorts, even in the Just Intonation scale it is out of wack. The hammers of our beloved pianos are usually constructed so that the hammer strikes near a node for this 7th overtone in an attempt to diminish its influence. Seven maybe lucky elsewhere but as a harmonic it is in ill favor!

So holding down the key that naturally produces “A110” you are able to hear the harmonic series by pulling each drawbar individually. How can we gain a working knowledge of the 9 harmonics (drawbars) as laid out on the electronic Tone Wheel organ? Let’s have some fun while we learn what these pitch relationships mean to our ears.

Experiment:

Interesting and fun fact: we will often use the trumpet, and its family of relatives, as an example of an acoustic instrument that wears its mathematics on its size and shape. This family of “lip reed” instruments cannot play the fundamental, they start on the second harmonic. This is true of this family of horns. Ask any trumpet player about the harmonic series and they are likely to know the relationships of the math. We all know that the longer the pipe the lower the pitch that is available, the shorter the pipe the higher the pitch. And we remember that by changing how we blow the instrument we can change the harmonic that is sounding. The valves on a trumpet simply open holes that shorten or length the active pipe length. What about a bugle, it has no valves, how can it play all 12 tones?



Well, if you know anything about a bugle, you know it can’t. Without sophisticated valves dividing the length of the horn’s pipe into 12 equally pitched lengths, all pitch variation is the responsibility of the player’s control over the instrument’s “reed” or vibrating lips (oscillator) and the air forced between them. (In fact, a trumpet with 3 valves cannot finger all twelve tones, trumpet players also must be able to use the harmonic series to reach certain pitches… the fingering for G and for C is exactly the same, you have to “lip” that interval. They need to narrow the slit and increase pressure and intensity to reach the next harmonic in the series. We already mentioned that the trumpet family do not play the fundamental, their lowest pitch is the second harmonic. So they cannot produce the principal tone (fundamental) – the 8′ in our drawbar example…

Using just the 4′, the 2 2/3′, the 2′, the 1 3/5′, the 1 1/3′ Drawbars (the second through sixth harmonics) – hold a single Key, then by pulling them out one at a time – you can “play” the melody to every bugle call there is – using just the single held note and the drawbars… Bugle calls, you say!?! Starting with the 2 2/3 Drawbar – “play” Taps… Simply hold any key and use the 2 2/3 drawbar as the first pitch. As a musician you don’t even know how many of these you actually already know. You probably can’t identify them all by name (unless you were in the Service) but you’ve heard and recognize at least half a dozen… (Google: “Every bugle call”) Taps, Reveille, Charge, Retreat, etc., etc. Long after you think you’ve heard all you know, here comes another familiar refrain.

If you look at the math of these intervals (the distance between harmonics as you go up the scale) you have a fifth, a fourth, a third and a minor third. It doesn’t take a Mensa to guess the next higher harmonic intervals will be smaller, and smaller. And thus is the harmonic series. That first interval, between the fundamental (the one the trumpet cannot do) and 2nd Harmonic is an octave. Octave-fifth-fourth-third-minor third…

In an attempt to recreate different sounds the Drawbars are added together at specific volumes to mimic the loudness of the harmonics in the sound being emulated. Subtle changes to the level of an upper harmonic will change not only the sound, but how we feel about the sound. With Pipe organs there were attempts to emulate Flutes, Reeds, and Strings… the native organ tone was referred to as the Diapason. Whether or not we think a Pipe Organ did a good job of emulation, it was a massive piece of musical engineering and if you find any of this at all intriguing, try getting a hold of any Pipe Organ music (or better, go experience it live) it is well worth the effort!

You notice the 5 1/3′, the 2 2/3′ and the 1 1/3′ are all musical fifths in relation to the principal’s pitch and are themselves an octave apart. 1 1/3 x 2 = 2 2/3 and 2 2/3 x 2 = 5 1/3. Why we don’t as quickly recognize these numbers as related in the same way we see immediately the relationship between the 8′, the 4′, the 2′, and the 1′ probably has to do with our fear of fractions. But pull these fraction Drawbars one at a time and hear their octave relationship to each other.

Lastly, we have one more fraction that stands alone – the 1 3/5′ – the 1 3/5′ is a major third above the second octave up from the fundamental.

Hey, here’s an ‘audio’ age test: Use the reface YC front panel – push all the Drawbars in
Pull out just the 2′ and the 1 3/5′
This is a major third interval.
Lower the OCT slider -1
Set Percussion and Vibrato/Chorus = Off
No Distortion, no Reverb
Set a Rotary Speed = Off
Play the lowest “F” on the keyboard… Identify that sound? These two harmonics played from the single key-on make a very recognizable sound (if you still have a land line telephone).

If you know what that is, besides two sine waves a major third apart, you were born before the age of the ubiquitous cell phone.
Yes, it’s the good ole North American Ma Bell dial-tone and was the sound you heard most often through your “good” ear (the one you naturally put the telephone up to…) the telephone’s set of sounds was completely made from sine overtones used in combination.

Now tap the “B”, a musical tritone above the dial-tone “F”: for the busy signal. (This was a tone you got when the person you were calling was already on the phone… before the invention of automatic voice mail and call waiting).

The front panel of the reface YC gives you the compelling real time interface with programming your sound as you go. The basic sound you get is built using the positions of your Drawbars. The basic tips you need to know from nature are as follows: It is fundamentally true (pun very much intended) that the lower the harmonic the louder it is within the sound. And while there are certainly exceptions to every rule, in general the higher the harmonic the less loud it is, is something you can understand is the natural order of musical sounds. So avoid being an “all or nothing at all” type user of the Drawbars. A touch of this or that, can make a huge difference in the sound, learn to listen for the contribution of each of your harmonic generators (er, Drawbars).


The Rotary Speed Control is as much apart of these classic organs as anything. The Pipe Organ included an actual room – usually a cathedral to help resonate its sound, the electronic organ’s Rotary Speaker is a part of placing the organ in a lofty space of its own, and it is no mistake that this combination is so very endearing to the overall performance of the electronic organ as an instrument. It is the cathedral, the acoustic environment that enhances the presence of the organ as an instrument. Learn to ‘work’ the Speed as apart of your performing. Just as you must learn to adjust your loudness with an Expression Pedal. What the Sustain pedal is to an acoustic piano, the Expression pedal is to an electronic organ. Not that they perform the same function but they are essential tools. To control loudness on an organ, you use the SWELL pedal, Pianoforte (Italian for soft-loud) was the first keyboard to have dynamic control via the keybed. Organ Volume is all about the Foot Pedal. Playing without one, well, it just isn’t done. It just isn’t!

To feel the full effect of the Rotary Speaker, you should always connect your instrument to a stereo sound system. The movement, the swirling motion is only felt in stereo… stereo is a situation where you have two speakers and the sound in each can be different from moment to moment. To give the illusion of movement stereo is a requirement. You can feel it in the reface YC’s own speaker system, what a difference stereo makes. Switch the Rotary Speed from Fast to Slow, then from Slow to Stop and then from Stop to Off. OFF will put your instrument equally in both speakers (mono). All other settings will send different amonts to the Left then to the Right at any given moment.

Emulative synthesis

The mighty pipe organ with its complicated system of Stops (Stops are combinations of harmonics often grouped to recreate a specific type of sound) is the grand daddy to the electronic organ. While drawbars are individual harmonics that are used together create a complex sound, pipe organ stops are much more timbral groupings designed to emulate flutes, strings, and reeds. When you recreate the relative loudness of the various harmonics to the fundamental, you have effectively mimicked that sound… The more harmonics you are able to match the more you will capture the timbre of the instrument. Of course, there are other factors in addition to matching the harmonic structure (envelope for example). As we move through the backgrounds of the reface instruments, you will see the different approaches in how ‘sound design’ takes place.

An integral part of playing the “tone wheel”, “transistor” and/or “integrated circuit” organs of the electronic organ era was the real time interaction with the drawbars, the rotary speaker speed, and the swell pedal…at minimum. Of course, the real masters of the craft kicked bass (pedals) and walked the left-hand all night long! We’ll be posting programs for reface Capture and on the Soundmondo site that recreate the sound on classic songs from the past.

We have a series of individual tone generators (be they pipes in a Pipe Organ or individual drawbars in an electronic organ), each tone source is responsible for generating a single simple pitch. When playing a single key, a more complex sound can be made by adding another tone generator (drawbar), in this case adding another simple singular pitch. The pitch of this second tone is naturally mathematically related to the first. These mathematical relationships color the sound for our ears and brain.

The first pipe organs were huge room filling affairs that would literally surround the listeners in its sound. Like no other musical instrument, the organ was bigger than life. It was tasked with emotionally moving and inspiring folks. You were literally enveloped in the sound. It could be coming at you from all sides, as the room was designed to help support and direct the SOUND onto the listener. And as in no other musical instrument, the room was totally a part of the sound and experience. This is certainly part of the charm of the Rotary Speaker which goes hand-in-hand with the most popular electronic tone wheel organ sounds. It gives a miniature version of the room shaking Pipe Organ _ so it is no accident that the motion (Doppler effect) of the Rotary Speaker fits so well with popular electronic era organ sounds. The motion of the sound gives the listener some of that same bigger than life feel of the mighty Pipe Organs.

A pipe of a particular length could make a tone of a specific pitch. The longer the pipe the lower the note; the shorter the pipe the higher the pitch of the note… We all know this from having blown across the opening of an empty bottle: The bigger the bottle the lower the pitch. That’s math at work. With absolutely no talent, the average person is able to get at least two tones out of blowing across the open end of a bottle. The easiest pitch to get is called the “fundamental”. Fundamental is the term used for the waveform that resonates most readily in the system. The next easiest pitch to get is quickly found by increasing the energy of your blowing and restricting slightly the slit you are passing air from (increasing its speed and intensity) suddenly out jumps a different, but related pitch. This is called the “second harmonic”. And to our ears it is the same note only higher in pitch – it has doubled in the number of vibrations per second – it has gone up one octave. The musical math is in action…

f = Fundamental
2f = (two times f) second harmonic (up one octave)

Let’s speed this along and bring in some mildly technical terms. You’ve heard them all before, but we will relate them to musical concepts you definitely know.

Integer – a whole number like 1, 2, 3, and so on.
Fraction – a number with a remainder, stuff left over, does not divide evenly… 1/3 (one third), 9/8 etc.
Cycles per second – a measurement of pitch, as in the “A” above middle “C” is “A440” where 440 is the number of vibrations per second. Also called Hertz (by audio folks).

We need these definitions and concepts to talk about harmonics.

• Harmonic is a whole integer multiple of the Fundamental.
• SubHarmonic is a whole integer subdivision of the Fundamental

If we find out that it takes an 8 foot long pipe (written: 8′) to recreate note middle “C” then a 4 foot (4′) pipe of the same material will produce a note an octave higher. And it will be true that each time you double or halve the length of pipe you will have shifted the fundamental by an octave.

The Drawbars that are octaves to the Fundamental (Principal) 8′, are 4′, 2′ and 1′ (these are white ones at left), while the 16′ (called SubOctave) is technically the SubHarmonic to the Fundamental (Principal). There are 2 SubHarmonics; they are the two brown drawbars.

8′ = f Fundamental, say we play “A1” “A110”
4′ = 2f Two times the Fundamental A220
2′ = 4f Four times the Fundamental A440
1′ = 8f Eight times the Fundamental A880

Push all 9 Drawbars up – no sound
Set Oct switch down -1 (if you have a reface YC) and hold down the lowest “A” key
Pull out just the 8′ _ you will hear A110
Push it back, and pull out the 4′ _ you will hear A220
Push it back, and pull out the 2′ _ you will hear A440
Push it back, and pull out the 1′ _ you will hear A880
Finally push it back, and pull out the 16′

16′ = f/2 Fundamental divided by two “A55”

What you experience as you continue to hold the key is the original note you played when you pull out the 8′ and you hear the mathematical doubling of the number of cycles per second as you engage the next whole integer drawbar. Double the frequency means go up one octave.

Now try pulling all these related Drawbars out 16′, 8′, 4′, 2′, and 1′ together. Try different amounts of each – making different combinations. You are changing the identity of this sound. The 16′ + 1′ gives a very recognizable organ tone used in Bossa Nova and in Reggae … These combinations of relative volumes gives us a unique overall tone. In fact, you hear the total thing and not so much the individual components, particularly when you start performing with the sound. Holding a single note invites analysis, but when placed in motion, as when executing a “musical phrase” the composition of the sound is accepted as a whole entity – and we become less cognizant of the individual loudness of each of the harmonics (overtones). This acceptance of the sound as a whole, is key to sound programming. Listening to the individual components separately, gives us a peek-behind-the-curtain… we can see how the wizard pulled off the magic. But as you begin to change the relationships of these related tones, you can see that it profoundly changes the character of the tone. By being the same pitch in different octaves this gives a strong sense of the fundamental – the other drawbars footages will completely put a new shade, a new color to the sound.

Drawbars with Fractions in their Name

But what about those other Drawbars? The ones that have fractions… Where’d they come from? Why did they choose these particular fractions? Oh no, more math! I promise we will avoid any heavy stuff (for now).

Here let’s introduce some concepts about how we hear as humans. We are able to identify sounds by cataloging in our brains thousands and thousands of bits of data. Like remembering names and faces, your brain can identify the relative loudness of the different frequencies that make up a sound. These “harmonics” become the way we identify and categorize musical tonalities, voices, sounds in general. We can make remarkable guesses based on just small bits of information. We recognize peoples voices, and can even read intent into how their sounds are shaped.

Those different frequencies making up the single note are harmonics. The harmonic series is a naturally occurring series of ascending pitches such that they are whole integer multiples of the fundamental.

We’ll use “A” because the math is easy enough to do in your head.

If “A110” is our fundamental we will find the harmonic series by multiplying 110 x 2, 110 x 3, 110 x 4, and so on.

So the mathematical harmonic series
Fundamental (1st Harmonic) 110 = pitch is “A” (principal)
2nd Harmonic 220 = pitch is “A” one octave
3rd Harmonic 330 = pitch is “E” one octave + fifth
4th Harmonic 440 = pitch is “A” two octave
5th Harmonic 550 = pitch is “C#” two octave + major third
6th Harmonic 660 = pitch is “E” two octave + a fifth
7th Harmonic 770 = – – – pitch is two octave + a pitch just flat of G, but definitely sharp of F# — (not used as a drawbar)
8th Harmonic 880 = pitch is “A” three octaves above principal

_55 A (sub harmonic)
165 E (sub harmonic to the 3rd harmonic which is musical fifth above the Fundamental)

Musical intervals of a fifth (very supportive to the fundamental) and a major third add harmony within the generated tone. Learning to listen for this, is a key in sound designing. Often you only want a very little bit of one of these other pitches (harmonics) in your sound. As we go on we’ll begin to see how tones that are not even generated directly can appear as part of the overall sound.  

The 7th Harmonic is not used… the nine drawbars of the tone wheel type organ are derived from the 1st, 2nd, 3rd, 4th, 5th, 6th, 8th plus the SubHarmonics for the 1st and 3rd Harmonic. A decision to give the instrument a solid foundation: by doubling the root+fifth interval this gives plenty of support at the bottom of the frequency spectrum. With the harmonics available to you via the Drawbars you are able to construct various organ programs (setups).

All the drawbars are connected to individual sine wave generators. As we’ll see this is significant. The sine wave being the building block of all wave shapes.

Here are some interesting facts. The pipe organ original used cyclindical metal and wood pipes to create its tones… Which were technically close to sine waves. The mighty Hammond organ used tone wheels (spinning disks in front of a magnetic pickup) to generate its sine waves. In synthesizer terminology this is referred to as “additive synthesis” – the combination of these individual sine waves are accepted by our ears and brain as a complex wave shape.

Motif XS/XF, S90 XS/S70 XS, MOXF Experiment
In the Motif XF, S90 XS/S70 XS and MOXF represented in the Preset Wave ROM are Waveforms of each of the drawbar footages. And you are given combinations, for example, the cursor highlights the “Draw 1+3” which combines the first and the third drawbars: the 16′ and the 8′ (SubHarmonic and the Principal) to a single Waveform. A “Draw 2+4” combination, the second and fourth drawbars (the Quint and the Octave). This is done because on the VOICE engine of the synthesizer there are but 8 Elements. So the combination Waveforms can be put to good use when attempting to recreate a specific drawbar configuration. The 8 Elements are not drawbars – they can act as individual level tone source controls which can give you the essence of what a drawbar does – but these are synthesizer emulation.  

The Waveforms with “Of” in their Name are stored with out the initial Attack portion. Those with “+” or “-” in the Name are shifted in phase and are provided to expand the subtle behaviors when combining Waveforms to build a Voice.

The combination Waveforms (the lower drawbar tones) are considered the “foundation” or base upon which you build your organ sound. The upper drawbars brighten the sound and add dazzle.

Choose your 8 Waveforms wisely if you are going to construct a specific drawbar setting using the VOICE architecture in these synthesizers. No you will not have the exact same 9 separate controls of an actual organ, you are creating an emulation of the real thing. As you can tell, if each Element is used as an active tone source, building an organ tone is very expensive in terms of polyphony. Organ Voices setup to be drawbar emulations are the most polphony intensive that you can make on these sample-playback engines. 

Experiment with the VOICE: “ALL BARS PERC AF1&2”
It contains the Draw 1+3 combination, the other footages are your set of drawbars
In VOICE mode:
On the Motif XS/XF: the Control Sliders 1-8 become Element Level
On the MOXF: Press the both KNOB CONTROL buttons simultaneously (all 6 LEDs light) the Knobs 1-8 become Element Level
On the S90 XS/S70 XS: Press the Control Slider button repeatedly until the LED goes OFF, the CS are now Element levels 1-4 or 5-8

Next Article: The Father of the Synthesizer III