It's a curious concept, it took me a while to get used to when I started singing lessons.
When you learn an instrument, while you're learning the basics of your technique, the emphasis is on something totally practical. Press these keys in this order, play your scales with this fingering, and so on. You don't generally start getting to things like interpretation and the 'feel' of the music until you've got those basic manual skills in place and you've learned to coordinate your fingers with the keys and the notes on the page. Even loud and soft are initially practical issues, not interpretive ones.
But when you learn to sing - properly, I learned classical technique even though I ended up branching off into jazz and blues - you don't have that basis to start from. You don't have the instrument in front of you, on which you learn the practicalities of playing and then you start making music. All you have is yourself, your own ears and voice, and in order to learn technique, all you have to go by is the way making any given sound makes you feel. You do the instrumental method backwards, in a way - you learn how the notes feel and you work your technique from that. Sung properly, you can feel each note resonate in your body, and you learn to pitch notes by where you feel that resonance - starting in your chest and moving up through your neck and into the cavities behind your mouth and nose and into your forehead, as you go higher in pitch. You can feel when a note is right, and then you learn to vary that feeling to start playing with tone and dynamics.
That's what I mean by singing being less quantifiable... it feels different to every singer. At the basic level every pianist plays pretty much the same, they press the same keys, often use the same fingering for any given piece. But every singer feels their voice differently... even if two singers use the same music at the same pitch their experience of singing that music will be different - any given note will resonate in a different place in their bodies, it will be physically different for them.
That's why when you have singing lessons with a good teacher, the basis for your lessons is always about how making a certain sound makes you feel and how you interpret that feeling - you have to be able to put an image or a name on that feeling so you can reproduce it reliably. Coming back to the idea of sound having shape and colour... for instance my voice teacher taught me to project my high notes by visualising the sound as a search light or a laser beam, to make the sound penetrate, and then we changed the colour and direction of the laser beam to vary the tone and dynamics. If you want to teach that to a pianist, you don't teach them about imaginary laser beams, you teach them about how to press the key and/or pedal to make the piano sound louder.
Singing is a completely individual experience right from the start, your voice is your own and you feel it and interpret it in your own way based on your own anatomy and experience. I don't think most pianists can say the same about their initial training. That's why there are endless tutor books of piano exercises as they're all based on manual dexterity, teaching you to press the keys, but there are relatively few voice exercises - they're all pretty much the same, based on scales in different patterns and pitches and using different syllables, but the emphasis isn't on pressing keys, it's on how that scale makes you feel - and then you carry that straight into 'proper' music.
The most basic exercise most singers use is scales in fifths - C D E F G F E D C, done up and down by semitones through the range of the voice with different vowel sounds... it's really simple, but because your focus is on the feeling of singing the scale in order to produce different techniques it's capable of pretty much infinite variations. If you can learn to feel a scale as you play it, they're not such a chore!
Topic: Colour in music.