4 ms·
The interactive harmonic lattice, with the commas clickable and audible, is first rate and is the best interactive illustration of JI problems I have yet seen.
by thrtythreeforty 2y ago
The interactive harmonic lattice, with the commas clickable and audible, is first rate and is the best interactive illustration of JI problems I have yet seen.
It is not quite clear from the explanation, that since the "3" direction is also dividing by 2 implicitly, the note confusingly labeled "3" is really just 3/2 - the perfect fifth. Similarly, the note labeled "5" is actually what we hear as the 12TET major third - clarifying a couple of examples on this lattice (or playing a chord) would be good.
Then, the thing I think that might help is driving the point home a little more by creating a comma by hand - a "knight's move" to another tile 5 horizontal and 3 vertical, creates a ratio that almost but not quite undoes itself. The (unwieldy) math is 1*3*3*3*3*5*5/2/2/2/2/2/2/2/2/2/2/2 = 0.9887, and this is what creates the commas in JI. Hiding the octave transpositions, while making for a neat visualization of the lattice, confuses the underlying issue.
- pierrec 2y agoI'm now realizing this and I totally agree that hiding the octave transpositions might make things confusing. Maybe this could be clarified by having a first lattice where this adjustment is not made, and everyone can observe how frequencies rapidly become extremely low or high, maybe to the point of being inaudible. Then we can ask "how can this problem be solved?" and introduce the concept of pitch class lattices where everything is transposed into one octave. Regarding intervals, I've always seen the irony and should probably mention it. Yes, the classical concept of fifth is related to the 3-ratio, while thirds are related to the 5-ratio. I'd argue this falls under the "empty your cup" category, but yes, leaving it untold probably doesn't help with understanding.
- thrtythreeforty 2y agoTo continue with an empty cup philosophy while still mentioning intervals, you can just posit "humans like how these 5- and 3-ratio intervals sound" and play chords using them to demonstrate. Then you don't need to handwave why this particular lattice was picked, and you can draw a comparison to 12TET's third and fifth.
- pyinstallwoes 2y agoWhat are your thoughts on the fringe 432 theory, but the actual roots of it in relation to the geometric significance towards whole number ratios and then what is never discussed: the tuning associated with it?
- bongodongobob 2y agoIf you're talking about using 432 Hz vs 440 Hz it's nonsense. You could pick any frequency you want. The frequency you pick to tune an A to is arbitrary.
- pyinstallwoes 2y agoYeah but you don't have the same knowledge apparently.
- bongodongobob 2y agoSame knowledge of what?
- munchler 2y agoIn other words, 3 * 3 * 3 * 3 * 5 * 5 is 2025, which falls well short of 11 octaves (2^11 = 2048). No series of 3's and 5's can ever multiply to a power of 2.