how to use mutation stops?

When I first sat down at our church's unused organ and experimented with stops, I noticed at one point a tuning "problem" which I traced to a stop with a fraction on it. I was hearing a 5th in there somewhere, and thought the stop was defective. Certain chords did not sound good. I later learned from the internet that it was designed this way - on purpose! Imagine that! Well, I resolved to never use such a ridiculour stop. But now I'm wondering if I'm being ridiculous. After all, centuries of organ builders can't be wrong. How do others use these stops - mutations? Is it worth dedicating a tab or a piston to one?

Fermata:
Here's a link to some basic stop/registration info. Hope this helps you in getting started!
-Jerry

http://pipe-organ.com/downloads/registration.pdf

Mutation stops serve to strengthen certain harmonics.

With any tone that we sing or play, harmonics can be heard. The first harmonic is the fundamental tone that we actually try to play or sing. The second harmonic has a frequency that is twice as high, and it sounds a pure octave higher. The third harmonic is thrice as high, and sounds an octave and a pure quint higher. The fourth harmonic sounds two octaves higher. The fifth harmonic two octaves and a tierce.

Now you'll notice that many organs have a Principal at 8'. This means that the largest pipe of this rank has a length of approximately 8 feet. Now on the same organ you might find an Octave at 4'. Its pipes are twice as short, so it sounds twice as high - what interval does that corresponds to? Indeed, it strengthens the second harmonic, which is an octave. Of course you guessed that already from the name of the stop.

The Octave 4' is not considered a mutation stop though, because 4' is an integer. So let's continue to the Quint 2 2/3, which is a mutation stop. Where does that fraction come from? Well, divide 8' by three and you'll get 2 2/3'. Its pipes are thrice as short, and it sounds thrice as high, so this one strengthens the third harmonic - which sounds an octave and a quint higher than the fundamental. You see? It's all in the name.

Now it shouldn't be hard to guess what a Superoctave 2' and a Tierce 1 3/5 serve for. They strengthen the fourth (8/4 = 2) and fifth (8/5 = 1 3/5) harmonic respectively. The Superoctave is not a mutation stop (integer), the Tierce is.

What's the difference between the (super)octave and the mutations? The octaves mainly serve to strengthen and brighten the overall sound. The mutations are mainly broadening and filling the overall sound.

But hey, something is going on when you play chords. When listening closely, you hear all kinds of dissonants and beatings, even if the organ is perfectly tuned and even when you don't play any dissonants. What's that?

Well if we play chords, each tone of the chord has its own natural series of harmonics. When playing those individual tones in chords, the harmonics start to collide.

To make it even worse, organs are not tuned to perfect intervals (it is actually impossible to do so for all intervals, but that's a different story which is even more complex), but the harmonics do sound at perfect intervals. So the imperfect quint interval that you play in a chord collides with the perfect quint interval that is naturally included in the harmonic series of any pipe that you play. This creates a beating. The effect is (in equal temperament) even worse for tierce intervals.

Now, the harmonics that are already present naturally, can be strengthened by mutation stops, making the effect more pronounced, and in some cases so much pronounced that you start to doubt if it sounds acceptable.

So if I were the first scientist to discover the principles of sound, I would say that the thought of making polyphonic music is just crazy. With all those colliding harmonics, it becomes a mess to play or sing almost any stack of tones (chords). The only thing that I would recommend is to try sequences of tones (melodies). But then only in non-reverbant spaces, because the harmonics in the reverb of one tone would collide with the harmonics of the next tone.

Luckily, history took a different course.

[mdyde]

[Topic moved here.]

Mutation stops serve to strengthen certain harmonics.

With any tone that we sing or play, harmonics can be heard. The first harmonic is the fundamental tone that we actually try to play or sing. The second harmonic has a frequency that is twice as high, and it sounds a pure octave higher. The third harmonic is thrice as high, and sounds an octave and a pure quint higher. The fourth harmonic sounds two octaves higher. The fifth harmonic two octaves and a tierce.

Now you'll notice that many organs have a Principal at 8'. This means that the largest pipe of this rank has a length of approximately 8 feet. Now on the same organ you might find an Octave at 4'. Its pipes are twice as short, so it sounds twice as high - what interval does that corresponds to? Indeed, it strengthens the second harmonic, which is an octave. Of course you guessed that already from the name of the stop.

The Octave 4' is not considered a mutation stop though, because 4' is an integer. So let's continue to the Quint 2 2/3, which is a mutation stop. Where does that fraction come from? Well, divide 8' by three and you'll get 2 2/3'. Its pipes are thrice as short, and it sounds thrice as high, so this one strengthens the third harmonic - which sounds an octave and a quint higher than the fundamental. You see? It's all in the name.

Now it shouldn't be hard to guess what a Superoctave 2' and a Tierce 1 3/5 serve for. They strengthen the fourth (8/4 = 2) and fifth (8/5 = 1 3/5) harmonic respectively. The Superoctave is not a mutation stop (integer), the Tierce is.

What's the difference between the (super)octave and the mutations? The octaves mainly serve to strengthen and brighten the overall sound. The mutations are mainly broadening and filling the overall sound.

But hey, something is going on when you play chords. When listening closely, you hear all kinds of dissonants and beatings, even if the organ is perfectly tuned and even when you don't play any dissonants. What's that?

Well if we play chords, each tone of the chord has its own natural series of harmonics. When playing those individual tones in chords, the harmonics start to collide.

To make it even worse, organs are not tuned to perfect intervals (it is actually impossible to do so for all intervals, but that's a different story which is even more complex), but the harmonics do sound at perfect intervals. So the imperfect quint interval that you play in a chord collides with the perfect quint interval that is naturally included in the harmonic series of any pipe that you play. This creates a beating. The effect is (in equal temperament) even worse for tierce intervals.

Now, the harmonics that are already present naturally, can be strengthened by mutation stops, making the effect more pronounced, and in some cases so much pronounced that you start to doubt if it sounds acceptable.

So if I were the first scientist to discover the principles of sound, I would say that the thought of making polyphonic music is just crazy. With all those colliding harmonics, it becomes a mess to play or sing almost any stack of tones (chords). The only thing that I would recommend is to try sequences of tones (melodies). But then only in non-reverbant spaces, because the harmonics in the reverb of one tone would collide with the harmonics of the next tone.

Luckily, history took a different course.

josq, that was nicely written and is a far better explanation than I heard the first time around. He didn't specifically ask, but you could also expand on this with an explanation of mixtures and the resultant 32' ...

Also, combining those strange mutations you can obtain a nice solo CORNET stop:
8´+ 4´+ Nazard + 2´ + Tierce + trem (opt).

Also, combining those strange mutations you can obtain a nice solo CORNET stop:
8´+ 4´+ Nazard + 2´ + Tierce + trem (opt).

Yes, that works great on some organs. But on a few I've noticed that this doesn't give enough "body" to the sound, organs with a real cornet seem to have a stronger sound most often, in my experience anyway.

Rule number one when using Mutation stops,
be sure that the True Harmonic Stops played with
the Mutations, are Louder than the Mutations !------( see below)

Or, when you are Playing in say the key of C,
the Organ will be usually sounding a Fifth above, say in the Key of G !

( [u]also avoid playing "Celeste" ranks by themselves[/u] as they are tuned a bit sharp intentionally !

So the imperfect quint interval that you play in a chord collides with the perfect quint interval that is naturally included in the harmonic series of any pipe that you play. This creates a beating. The effect is (in equal temperament) even worse for tierce intervals.

That's why stops like "Tierce" work better on organs that are NOT designed for "Equal Temperament"... which is very much a new-comer to the Organ World, and is distinctly out of keeping with the intrinsic Aesthetic of the Organ.

He didn't specifically ask, but you could also expand on this with an explanation of mixtures and the resultant 32'

Hearing the harmonics strengthens our sensation of the fundamental tone... so much so that it even works if the fundamental is absent. Deep notes on a 32' stop are barely audible, but would have a second harmonic at 16' pitch and a third harmonic at 10 2/3' pitch. If we have those two pitches available as stops, and play them together, it creates the rich impression of a 32' fundamental pitch being present (as if it were itself responsible for producing these pitches as harmonics)... even though it is not.

This can work two ways: either pull a stop labeled 16' plus a stop labeled 10 2/3'... or they may both be automatically included in a stop called "32' Resultant".

Mixtures just add lots of upper harmonics together, often with more than one pipe per pitch. They add brilliance. And as stated, they only work well when the lower harmonics are well-represented.

Well, now I'm all excited to try out that mutation stop after church tomorrow, which I have heretofore studiously cold-shouldered. I will try that cornet combo and see what happens. Its amazing what a little bit of education can do. Thank you, Josq, for your very informative post, it's really appreciated!

What are the must-haves, when it comes to mutations, the most popular ones?

Glad to hear my explanations are appreciated! So let me see if I can find time and inspiration to continue on the topic of mutation stops.

First, the Resultant Bass 32', or whatever the stop is named. As you all know, sound is air waves. Before we go to this deep bass sound, let's have a look at more common pitches. Perhaps you know that concert pitch is often defined as A = 440 Hz. What does that mean? Well, if we play an A on an instrument that is tuned to concert pitch, the instrument (strings or pipes or whatever) will make the air oscillate 440x per seconds. To write it more concise, the Hertz unit has been invented, so we can write 440 Hz. On top of that, you will find oscillations of the harmonics, so oscillations of 880 Hz and 1320 Hz and so on.

Now, a bass tone has fewer oscillations per second, for example 20 Hz for one of the lowest pipes of a 32' stop. What about the harmonics of this tone? The second harmonic be 40 Hz and the third 60 Hz.

Now we are going to remove this tone. Instead, we will generate two different musical tones. One of them, a 16', sounds in this case at 40 Hz, and the other, a 10 2/3', at 60 Hz. What will happen?

An oscillation can be represented as a regular pattern of peaks and dips. Perhaps from high school you remember the waveform patterns of the sinus and cosinus graphs. We have to add up two of these graphs, one with 40 oscillations and one with 60 oscillations per second. If the peaks of both graphs are aligned, we get an extra high peak. If the dips are aligned, it sums up to an extra low dip. If a peak of one graph aligns to the dip of the other, they cancel out.

Let's suppose the peaks are aligned at the beginning of the graph. An extra heigh peak results. How much do we have to move on before the peaks are aligned again? Try to visualize it. Here is the answer: 1/20 part of a second. After 1/20 part of a second, the 40 Hz tone has completed 2 oscillations, and the 60 Hz tone has completed 3 oscillations. The peaks are aligned again. So every 1/20 second we have an extra heigh peak.

There it is, the resultant: every 1/20 second, so at 20 Hz. Even though we removed the original 20 Hz tone, we get it back (in a slightly different form) by addition of a 40 Hz and a 60 Hz tone, in the form of recurring extra heigh peaks in the oscillations of the air.

See https://de.wikipedia.org/wiki/Residualton for a graph (using different numbers).

By the way, I do not reject the psychoacoustic explanation given by OrganoPleno. At this moment, to me it is an open question where physics ends and where psychology begins in the realm of music, and what the role is of the physiology of the ear.

What are the must-haves, when it comes to mutations, the most popular ones?

Most important is the "Quint", at 2 2/3', which plays well along with a comparable voice at 8'. Actually, stops at this pitch can have different names. The ones called "Quint" are typically voiced as Principals, and would play well with an 8' Principal (which may also be called Diapason, or Prestant, or Montre). Others may be voiced as a Flute, and may be called Nasard or Nasat. These would play well along with an 8' Flute.

Quints can also occur an octave higher, at 1 1/3'. In French, these are called Larigot (typically a Flute voice). In English, they may be called Nineteenth (typically with a Principal voice).

The second most relevant would be the Tierce, at 1 3/5'.

Some organs have a stop called "Sesquialtera", which is a compound stop containing pipes at both 2 2/3; and 1 3/5' pitch for every note. Played together with Stops at 8', and 4', and 2' all together (preferably all voices as Covered Flutes which are often called Gedeckt or Bourdon or Stopped Diapason)... this can make a very fine Cornet voice. It is so rich in upper harmonics that the complex combined sound strongly resembles a Reed, even though no actual Reed Stop (such as Trumpet or Dulcian) is drawn.

By the way, I do not reject the psychoacoustic explanation given by OrganoPleno. At this moment, to me it is an open question where physics ends and where psychology begins in the realm of music, and what the role is of the physiology of the ear.

I don't think there is any discrepancy here. What we hear (perceive) is determined by the physiology of the ear, which responds to the physics of sound, which follows mathematical patterns such as you have so effectively described.

At one level, music is ENTIRELY about Psychology. It is the task of the Artist to use mechanical devices (Instruments) so as to actualize the principals of Physics in such manner as to elicit the desired Psychological response in the Listener. This does NOT mean "no substance, all effect". Rather, it is that very Substance that produces the Effect.

Picking up on the notion of a resultant 32-foot stop - I learned many years ago that the resultant 32-foot effect created by sounding notes of 16-foot and 10 2/3-foot pitches together is due to what is known as a "difference tone". In other words, sounding two notes together which are fairly close to each other in frequency results in the acoustic generation of a new tone whose frequency is the difference between the frequencies of the original notes.

For example, the lowest C at 16-foot pitch vibrates at 33 Hz. The lowest note (G) at 10 2/3-foot pitch vibrates at 49 Hz. The difference between 49 and 33 is 16 Hz - which is the frequency of the lowest C at 32-foot pitch.

http://peabody.sapp.org/class/st2/lab/notehz/

The same phenomenon also works an octave higher. 30 years ago I rebuilt a small 2-rank pipe organ for a reverberant monastery chapel. Originally the organ had 1 manual and 5 stops. With the help of a friend I converted it to 2 manuals and pedals, and redesigned the stoplist to draw 15 stops from the same two pipe ranks - Stopped Flute 8 and Fifteenth 2, each of 61 notes, fully contained within the console. I created a remarkably effective synthetic bass octave for a new 16-foot Bourdon stop on the Pedal by wiring the lowest 12 notes to sound two pipes - 8-foot plus 5 1/3-foot - from the Stopped Flute rank. The two real pitches at bottom C are 98 and 65 Hz respectively, creating a difference tone of 33 Hz. One visiting organist actually asked me where I'd hidden the new big pedal pipes!

This little organ has since moved twice, and is now one of two 2-rank extension organs in an organist's residence. There are some errors on the page below - the organ's first move was in 2000.

http://www.ohta.org.au/organs/organs/MayfieldDate.html

Andrew

Dear all,

I like to point You to an interesting article of Mr. Colin Pykett, who investigated the widely-believed "difference tone" effect of resultant stops (i.e. 16' + 10 2/3'). He derives that the resultant frequency one octave below the longer stop (32' taking the example above) does NOT carry any intensity (i.e. volume), since it was not actively generated by any sound source. However, the simultaneously sounding stops a quint apart will be modulated with a beating frequency (which is the correct term here) which equals that generated by a true 32' stop.
Depending on Your personal hearing this can indeed mimick a 32' effect, for some more, for others less convincing.
Those, who are hard to fool by this trick (like me) always hear the quint interval (i.e. the two notes) instead of the pure resultant frequency. Read the footnotes of Pykett's article to get a feeling how different individual hearing is and how difficult the field of pschoacoustics seems to be . . .
http://www.pykett.org.uk/resultantbass.htm

Best regards
Frank

Hello post: this topic has moved toward the interesting problem of 32´resultant. And I have I simple (or perhaps, silly) question about 32 resultant,please:
When real pipes when C and G (16´) are played simultaneously each pipe will produce an independent wave, so the resultant 32 is clearly perceived.
But in virtual amplified organs, does the mixed resultant in formed (constructed) in the cone of the speaker or in the air?
Thanks¡