It is commonly stated that in just intonation the pitch ratios should be simple, in the sense that a minor third of 6/5 is simple and acceptable, but a minor third at 32/27 is sometimes dismissed because the ratio is complex while we have 6/5 available.
Let's check tone E at 330 Hz and G at 396 Hz which have a pitch ratio of 396 / 330 = 6/5. If we use an alternative G with a ratio of 32/27 to E, its pitch becomes 330 * 32 / 27 = 391.111... Hz. The sixth partial sinewave of E is 330 Hz * 6 = 1980 Hz. The fifth partial sinewave of the alternative G is 391.111... * 5 = 1955.555... Hz. Those two partial sinewaves beat with an irritating rate of 1955.555... - 1980 = 24.444... beats per second: 32/27 is close to 6/5 (so it beats, instead of being merely dissonant) but it is not close enough (so its beating rate is too high to be agreeable). See also Beating and you can listen tho these different minor thirds here.
But there is a twist. The pitch ratio 135/128 (a chromatic semitone) is accepted in just intonation, while its pitch ratio is quite a bit more complex than 32/27. How can an interval with ratio 135/128 be acceptable? It does beat, most clearly in the lower octaves of the keyboard. But that hardly differs from semitones in any other tuning. So composers have learned long ago to avoid chords with semitones in the bass range.
So is just intonation practical? Not as long the theory sticks to simple whole numbered pitch ratios while actually the beating rates matter more.
On hearing a specific rising melodic interval, one has expectations of the second tone's pitch, for instance because of a life long exposure to 12 tone equal temperament. If in just intonation it turns out to be lower or higher, that can be irritating, no matter how simple or complex the whole numbered pitch ratios are. You can test your own expectations when you listen to the final cadence of Suite Gothique, Toccata by L. Boëllmann in the version that ends in the chord C-F♭-G instead of the traditional C-E-G.
Just intonation music may be impractical if many players and listeners are and remain annoyed by its difference with 12 tone equal temperament.
In any western music the general pitch is supposed not to drift up or down during a performance. 16th-century mathematician Giovanni Battista Benedetti devised a two measure chord sequence that, when repeated, causes the pitch to drift upwards in just intonation.
(see also Matrix Video)
If you don't notice the pitch rising, restart the fragment immediately after it ended. If you then don't notice a pitch difference between the end and the beginning of the fragment, you are advised to stop tormenting your brains by trying to understand what this website is all about.
The algorithm supporting the music on this website allows a very modest global pitch drift, but quite a capricious up and down drift in between. The algorithm inserts syntonic commas, perfect fifths of pitch ratio 40/27 and minor thirds of pitch ratio 32/27 a.o. to control global drift. Is all that allowed in practical just intonation?
Keyboard instruments, guitars and some other instruments can be adequately tuned to 12 different pitches per octave. A limitation to 12 pitches per octave is incompatible with just intonation except for the simplest music - not available on this website. Concert harps could go as high as 21 different pitches per octave and rare keyboard instruments go beyond that.
Bowed string instruments, slide trombones and the human voice can technically produce any pitch within their range, but do the musicians command their instruments to the extent that they can actually produce the precise pitches as required at any moment? Many a capella choirs and string quartets produce absolutely marvelous music, also in terms of tuning. But would that be just intonation in any variant? Measurements I know of reveal pitch ratios differing considerably from just intonation. A capella choir tunings often tend more towards 12 tone equal temperament than to just intonation.
So music played/sung in just intonation is rare (therefore impractical), now and in the foreseeable future.
Composers of most western music write down the notes without making any distinctions between the slightly different pitches that a note, say middle C, can assume in just intonation. There is no widely accepted notation for such distinctions anyway, which is not very practical. The precise pitches to be produced are left to the musicians to determine. Even with a suitable notation system, it would not at all be easy for a composer or editor to choose the exact right pitch for each note/chord.
Music in just intonation is not practical. This website seeks to change that.