But it is relevant because Nyquist performs operations on floating point numbers.
OK, I’ll answer this within the specific context of Nyquist programming:
Nyquist defines division by zero as an error. Nyquist is written in C, which defines division as:
The result of the/operator is the quotient from the division of the first operand by thesecond; the result of the%operator is the remainder.Inboth operations, if the value ofthe second operand is zero, the behavior is undefined
Ref. http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf Section 6.5.5 item 5.
To demonstrate the Nyquist definition, enter the following in the Nyquist Prompt and click the Debug button:
(/ 2.0 0.0)
For the integer version:
(/ 2 0)
If you wish to define a division function that behaves differently, you can do so like this:
(defun divide (a b)
(if (= b 0)
<your definition code goes here>
(/ a b)))
For example, you could define it as:
(defun divide (a b)
(if (= b 0)
(if (plusp a)
(- (log 0.0))
(log 0.0))
(/ a b)))
;Test it:
(divide 42 0)
But how would you multiply two stereo tracks? It’s impossible to somehow join them to make a quadtereo track.
Write the first track to disk (see: Nyquist Functions), then when processing the second track, read the temporary file back from disk (see: Nyquist Functions).
So this disk manipulation is the official method of simulating two stereo tracks joined into one quadtereo track?
It’s the way that I would multiply two stereo tracks.
An alternative way would be to split the stereo tracks, make a new stereo track from the two left channels, and another from the two right channels, process the two stereo tracks as described by Trebor, then pan the first left, and the other right, and mix.
If you know a better way to multiply two stereo tracks, do tell us.
And is it possible to recursively apply this disk manipulation to simulate a hexadecereo track made of two octereo tracks, in turn made of four quadtereo tracks in turn made of eight stereo tracks? Are hexadecereo tracks what professional music designers use all the time?
“Hexadecereo” is not a term that any audio professional would use. I’m assuming that when you write “hexadecereo tracks”, you mean “16 channel tracks”.
Some software does support multi-channel tracks (more than 2 channels), though in my experience it is far more common for professional music designers to use mono or stereo tracks when producing the music. If a multi-channel sound file is required, then that is normally achieve by mapping multiple mono / stereo tracks to the required outputs. Audacity currently supports only mono or stereo tracks, though multi-channel audio files may be created on export (see: Advanced Mixing Options - Audacity Manual)
Stereo could be thought of as two joined mono tracks with the first one assigned Left and the second one assigned Right.
Quadtereo is the concept applied recursively; two joined stereo tracks. Four channels: LL, LR, RL and RR. Because joining tracks is required for that Nyquist multiply script to work, allowing any two tracks of the same type to be joined leads to this. To convert quadtereo to stereo, the LL channel contributes 50% to the left channel, the LR channel contributes 1÷3 to the left channel and 1÷6 to the right channel, the RL channel contributes 1÷6 to the left channel and 1÷3 to the right channel and the RR channel contributes 50% to the right channel.
Octereo (LLL, LLR, LRL, LRR, RLL, RLR, RRL, RRR) and hexadecereo (LLLL, LLLR, LLRL, LLRR, LRLL, LRLR, LRRL, LRRR, RLLL, RLLR, RLRL, RLRR, RRLL, RRLR, RRRL, RRRR) is what happens if this recursion continues. Sixteen speakers arranged in a hexadecereo formation would form a circle. Indeed Audacity doesn’t support this kind of audio, although it can be simulated. Sphereo is when speakers are arranged in a sphere formation, covering all directions. Converting a top or bottom channel of sphereo to hexadecereo would result in, you guessed it, imaginary number samples. This is all mathematical.
I’m locking this topic as it has deteriorated into nonsense.
“Quadtereo”, “Octereo” et al are not real words. They are just made up by Piotr Grochowski.
For anyone interested in “Quadraphonic” sound, there’s an article on Wikipedia: https://en.wikipedia.org/wiki/Quadraphonic_sound