Ok, maybe I don't understand something basic here. Disregarding the whole dynamic range issue for the moment. The explanation of 24bit sampling as was presented to me by certain Audio companies about 6-7 years ago one of the points of higher bit rates is to increase the resolution of a digital sample and get it closer to an analog curve. If we imagine a normal analog curve with a peak and a valley a 16 bit digital will sample that section into 16 distinct areas (rectangles) just like approximating the limit of a curve in Calculus. Everything not sampled by the rectangles under the curve is lost audio data. By sampling at 24 bits you get 24 rectangles which is 50% more data collection for the same sample section. Hence you create a smoother sampling with more resolution closer to the original analog signal. This sampling would apply throughout the entire sample regardless of the volume level or frequency in question right? I don't understand how the increased data or resolution attained throughout an entire song sampled at 24 bits only exists at a certain dB level? What am I missing here?
By reading the following along with your previous post:
"A set of digital audio samples contains data that, when converted into an analog signal, provides the necessary information to reproduce the sound wave. In pulse-code modulation(PCM) sampling, the bit depth will limit quantities such as dynamic range and signal-to-noise ratio. The bit depth will not limit frequency range, which is limited by the sample rate.
By increasing the sampling bit depth, smaller fluctuations of the audio signal can be resolved (also referred to as an increase in dynamic range). The 'rule-of-thumb' relationship between bit depth and dynamic range is, for each 1-bit increase in bit depth, the dynamic range will increase by 6 dB (see Signal-to-noise ratio#Fixed point). 24-bit digital audio has a theoretical maximum dynamic range of 144 dB, compared to 96 dB for 16-bit; however, current digital audio converter technology is limited to dynamic ranges of about 120 dB (20-bit) because of 'real world' limitations in integrated circuit design."
Its is clear that 24bit extends the maximum dynamic range to 144dB. But that is the maximum. I don't see anything that says increased resolution does not exists at any level below the maximum of 144dB. Are you saying at 96dB a 24 bit sample has the same amount of data and resolution as a 16 bit sample?
You're mostly right. With 16 bit you can have 2^16 different levels of intensity, meaning the the little rectangles drawn up like a riemann sum have 2^16 different possible heights and with 24 bit, they have 2^24 possible heights. You can have one, two, three etc all the way up to 65536, but you can't go higher than that or lower than zero, and all steps have to be in whole numbers. One or two, there can't be a 1.5. The minimum (no signal at all) and the maximum possible signal are determined by the quality and power of the equipment. 24 bit allows you to take more steps which are each 1/256th of one 16 bit step. Incidentally, the width of each rectangle is the sample rate. This extra data does capture more accurate and true to life approximation of the actual sound, besides the increased dynamic range. The real question Is how much of this data is audible to humans.