The noun definition in the dictionary will tell you that a Stable is a horse house, and that when used as an adjective it adds solidity, stasis, durability and/or changelessness to the object it modifies.
When I use this word for teaching or writing about voice, I want it to carry comfort as a connotation that you cannot disconnect from a house for horses. Horses are special animals that need a high level of comfort to be happy and healthy. This is an old understanding that would seem to be the inspiration for a really comfortable stable in Chantilly.
People and horses are very different, but they share a lot of things. A need/desire for comfort is among these common attributes. So it is nice to see that the first two Merriam-Webster dictionary examples of good adjective usage are about human interaction.
A stable human “Relationship” is not a changeless, static thing, but should qualify for labels such as solid and durable. How does a human relationship get to be solid and/or durable in a truly free society? I believe comfort has a lot to do with it.
A stable sound, line, phrase, interval or scale has at its core a message of comfort. Any message of discomfort, and there is either something wrong in the singer’s technique, or the singer is intent on injecting, depicting, or, more precisely put, interpreting the sound, line, phrase, interval or scale with discomfort.
The possibility that the student could be confused into believing that “Stable” means static, unchanging or perfect will most likely get that “discomfort” message going in a student’s sound right away.
So when I use the word “Stable” in my work, I mean to include comfortable as the standard adjective i.e.: Comfortably Stable. There is no perfect, unchanging or static “Stable” for the student to seek in the beginning of vocal studies.
There are many interpretive exceptions. I might cover one of them in a lesson that could fall between Lesson 10.001 and Lesson 12.300. It may be the easiest exception: how to depict a computer generated voice.