A quindecile is another astrological aspect of the harmonic row. The quindecile is an angle of 24° (twenty-four degrees) between two planets! The word quindecile is sometimes used wrongly to denote other angles, but the word quindecile shows already that it means to divide the circle by the number fifteen. Compare this with the other names of the aspects of the harmonic row! So the quindecile is only the aspect of twenty-four degrees and all other uses are wrong.
Divide the zodiac by twelve and you get a dodecile or the length of a zodiac sign. If you reverse this, then you get the length of twelve degrees by dividing the zodiac by thirty. If you divide the zodiac by a double of a dozen, this means by twenty-four, then you get half the length of a zodiac sign, which means that you get a length or an angle of fifteen degrees. If you reverse this, then you obtain an angle of twenty-four degrees or a quindecile by dividing the zodiac by the number fifteen. In the logic of the harmonic row is a dodecile a connection between the division by four and the division by three. Following the same logic is a quindecile a connection between the division by five and the division by three. I don’t arrive at any meaningful interpretation this way. The quindecile seems to be only playing with numbers. It is also noteworthy in this context that the quindecile is largest of those aspects, which are smaller than a zodiac sign and at the same time non-transcendent. This makes the use of the quindecile only more superfluous.
Most of the astrologers, who use harmonic aspects, use also the alphabetic zodiac, the reliably failure-producing idea that you wouldn’t need to distinguish between signs and planets and houses. A certain sign and a certain planet and a certain house would always form a set. These astrologers would love to force the aspects into this system too and this is the reason for them to use harmonic aspects. Each aspect is equaled with a planet in this system. This can only be done with enough planets, so these astrologers use either hypothetical planets or asteroids to obtain enough planets. If they use asteroids, then usually only the ex-planets. For some of these astrologers ends the harmonic row with the dodecile because aspects smaller than the length of a zodiac sign are unnecessary. For other astrologers ends the harmonic row with the quartdecile (if they don’t know Astraea) or with the quindecile (if they know Astraea) because they run out of ex-planets. Only few astrologers continue the harmonic row after the quindecile until the division by twenty. After that the distances become so short that the distinction from a conjunction or also the distinction between multiples of different harmonic aspects become nonsense.
There is no concept of the quindecile, which could be accepted as really serious. I see nothing else than some people playing around. So if you want to use the quindecile, then you should try playing around as its possible meaning.