In piano music how does one indicate that sequential notes in the bass clef are to be sustained with the fingers, not using the sustain pedal? For example, suppose I have the three sequential quarter notes C, E, G defining a C chord in 3/4 time in the bass and I want each note to be held to the end of the measure after it is struck, but I don't want to use the sustain pedal because I don't want the other notes in the treble clef to "blend" together. Is there a special kind of slur or other notation to indicate this? I know that one way to do this would be to break the three notes into three parts (i.e. use a dotted half note for the low C and then above this a quarter rest and half note of E, and above this a half rest and quarter note of G) but this seems like a far too complicated way of indicating what is a common style of playing a sustained "broken" chord note sequence. I also don't want to use arpeggio notation (wavy line) because I have a melodic line in the treble that interfaces precisely with the base notes. Can anyone help?
My answer is ultimately similar to Bob Broadley's, but has one difference that can make for much more readable scores in slightly more complex situations. This is the standard notation for broken held chords like the one you describe, as recommended by Kurt Stone and Gardner Read:
The difference here is that you don't rewrite any of the held notes until the chord is complete. For your specific relatively simple case, I don't think it's much better than Bob's. However, in an even slightly more complex situation:
the readability can be greatly enhanced. One of the things I like most about this notation is that it's fairly clear, even when the pianist hasn't seen it before. I use this notation in a lot of my piano music, and most pianists don't even bat an eye because they've seen it before. The few that haven't still immediately guess the meaning. The notation you describe in your question will eventually be figured out, but looks so much more complicated than the actual method of performance that it can be annoying. Same thing, albeit to a lesser extent, if you rewrite each tied note with each new note entrance. In more complex situations it can become difficult on first glance to ascertain which notes are new and which are being held-over.
Sometimes it will be obvious to a performer that you need to sustain notes that together outline one particular harmony (a single triad, for instance). If you want to make this explicit, though, you could use notation such as the following:
I'm not sure that this is used that much in piano music, probably because the pedal will produce the required effect (although I understand why you don't want to ask for pedal use here). However, it is a common way to show exact note durations in arpeggiated guitar music.
Also, if you want to make it clear that no pedal should be used, you could write senza ped., in addition to the notation above.
You can use a Tie to sustain notes in this manner.
There is more here: https://en.wikipedia.org/wiki/Tie_(music)