Music is not mushy, not all the time. Speaking of time, time is mostly very consistent and even. You can slow it down – ritardando. You can speed it up – accelerando. Still, it is mostly very consistent and even. Time is quantifiable and measurable. Within time are rhythms which also are very mathematical and are stated as fractions. Notes are given values as to how long they are sustained: whole, half, quarter, eighth, sixteenth, thirty-second, and so on. Sometimes they are one and a half times their value or are tied to other notes and the two values are combined to create that specific endurance of tone.
Even when a singer is singing rubato and is stretching or compressing note values or speeding them up or slowing them down, the time of the music usually is remaining constant. The singer, if a great singer, will know that the time is consistent and will have a sense of that time while simultaneously singing ad lib instead of mechanically interfacing with the time of the music in a strictly mathematical way. Time for the soloist can be alterable and malleable and is acceptable as long as the singer has a solid sense of where the time actually is.
Pitch is also mathematically measurable and is based upon a specific pitch, A, vibrating at 440 times per second. Speaking of math, up an octave is another pitch vibrating at 880 times per second. An octave is the eighth pitch, along the pattern of a scale, from the starting pitch. Down an octave from A 440 is the pitch A 220. Here we have the relationship of octaves, being half or double from any given note regarding the speed of vibration. There is a center of pitch. A faster vibration than the center is called sharp and a slower one is called flat. A note is like a dollar or a euro, in that it has 100 cents. The center is the “correct” pitch.
Some musical instruments have fixed pitches, such as the pianoforte, which we simply call a piano. A tuner can alter the pitches, but the player of the instrument usually does not, at least while playing. An electronic keyboard may have a pitch bend wheel on it, affording the player options not available on a standard acoustic piano. When a singer must interface well with music accompaniment, the singer must use hearing, the perception of pitch, of musical intervals, and instantly execute without resorting to analysis or other thought processes. A singer can bend pitch, slide up to a note or down off a note but must always be fully aware of the pitches in the accompaniment or there will be intonation problems.
Music is mathematical and is mathematically measurable but that does not make it mechanical, necessarily. There also are the possibilities of the loudness of tones being variable, from very very very soft -ppp to very very very loud -fff. Pianississimo to fortississimo and potentially softer or louder than those, with all variables in between.
Music is mathematical, mushy, and malleable, so to speak. There are many examples in many styles of the possibilities and there also appear to be infinite possibilities in the arrangements of pitch, durations, time, volume levels, instruments, and everything else. It is the mathematical aspects which have brought about instruments of measurement of time and pitch, musical instrument digital interface (midi), and digital recording of music. Math isn’t bad, but it is a point of stability, to be found in the morass of music. For a singer, it is all something to be aware of, but most of the time a singer is quite organic, bringing life to the party of music.