Nice introduction to Mixtures and Mutation stops

I don't know.  I am just working my way through these videos.  I am using my piano with keyboard splits, and adding my small CME X-Key 37 keyboard as another manual to fool around with, giving me two manuals and 'keyboard-operated' pedals, plus linking two of the manuals with a coupler 'pedal' in Organteq.

In Organteq, the V (which breaks on F) and III (which seems to break on C but it's a little harder to tell) Mixture have breaks, while the CV has no breaks and is the full compass of the instrument.  Normally Mixtures are combinations of very high pitched Mutation stops (say 2 2/3' and 1 3/5' or higher), which serve two basic purposes to give the lower notes on manuals access to some of the highest notes on the instrument (think of it as a high octave coupler) and to--as he says in the video--crown the sound of the other stops, or as I like to think of it, get the richest organ sound.  It crowns the sound by reinforcing and voicing the overtones on the harmonic series.  The roman number tells you how many ranks of mutation stops follow the harmonic series, so a "V" has up to the fifth overtone of the harmonic series while the "III" stops at the third overtone.  This page helps a lot in understanding the relationship between mutations, mixtures, and pipe length: https://www.die-orgelseite.de/fusszahlen_e.htm

This is why there are rarely numbers greater than six or lower than three on most organs--even the largest.  A numeral two would simply be a tierce stop (a simple fifth mutation in the harmonic series--the 2 2/3' length), and anything over number six (the quint) is the minor seventh overtone which is rarely useful or desirable (2 2/3+2+1 3/5+1 1/3+1 1/7).  While I've seen mixtures and regular stops of 1/2' they simply follow these same rules of sizing, just divided by another octave or two (which is usually little more than adding a dog whistle to an organ).  Here's an organ stop list that shows basically everything you can do with a mixture: https://www.thetabernaclechoir.org/cont...016-v1.pdf

The breaking means that some or all of the ranks are just an octave so the lowest and highest note of a given pitch will open the same pipe in that rank: the closest midi equivalent I can think of would be coupling a large piano keyboard with a single octave keyboard, such that whatever note or notes are played in whatever range on the piano (say low f and high a), will trigger the key you press on the single octave (the only f and a that the smaller one has).  It allows the organ builder to save on space--since ranks in mixtures can be smaller (and mixtures can take up tons of organ loft space and take the longest to tune)--and allows the organist access to fixed higher pitches from anywhere on the manual--much like a three or four octave coupler.

In practice, you leave mixtures to the last part of your registration, so they're like an icing on a cake, you don't start there and put the cake inside the frosting later.  Normally, any forte registration will include multiple mixtures over the top of 16+8+4+2 stops.  To test how this sounds and why you save them for the last registration decision you make, apply a 16' and Mixture with breaks (III or V) and see what it sounds like: you'll have a strong treble sound alongside the deep bass sound but it will be weak in the middle of the sound and easy to hear the breaks, but if you add 8+4 and maybe a 2' or 1' (though some think of 1' as a mutation stop because of high-pitched it is), you'll have a very full, rich organ sound.  Another useful experiment is to open all stops but the mixtures and then add the mixtures during playing.  The mixtures are designed to be powerful enough, that you can add them at the end of a forte passage and still hear them being added to make a fortissimo passage (this is largely because of the breaks and the number of high-pitched pipes and ranks that get added).  This effect is especially noticeable in contrapuntal music like a fugue, because the bass is suddenly much louder (with all of these extra high pipes) and it's using different pipes than the higher voices, which may be higher than the upper voices and therefore even more audible.

I find in my own registrations that I'm much more like to use a mixture than a mutation, but both should be added in the last step of planning a registration (which they'll cover in the later videos on Registration in this series) since 8+2 2/3 rarely sounds good while adding more octave stops and more stops of the same length like 16+8+8+4+2+2 2/3 will likely sound excellent in nearly any combination.