josq wrote: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.
profeluisegarcia wrote:Also, combining those strange mutations you can obtain a nice solo CORNET stop:
8´+ 4´+ Nazard + 2´ + Tierce + trem (opt).
josq wrote: 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.
sonar11 wrote:He didn't specifically ask, but you could also expand on this with an explanation of mixtures and the resultant 32'
fermata wrote:What are the must-haves, when it comes to mutations, the most popular ones?
josq wrote: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.
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