Learsfool – I appreciate your thanks and I’m grateful for your participation. Though our points of view never converged, I learned a lot from our debate along the way. Your final comments about training the ear, which I think of as training the brain, are well taken. Although we didn’t discuss it much in this thread, the ear/brain is probably the most important “component” in the system.
Cbw – I have given some thought to your suggestions for revising the working definition of ‘inaccuracy.’ Here is what I came up with:
INACCURACY: An alteration to information in a component or system that eliminates, conceals, or corrupts information about the music.
Defining 'inaccuracy' in this way raises the question: How does this new concept of 'inaccuracy' relate to the concepts of 'accuracy,' 'neutrality,' and ‘resolution’? I would like to offer a new proposal about the relations among these concepts. To begin with some definitions:
ACCURACY: 1. The relative amount of information about the music presented by a component or system, comparing output to input. 2. The degree of absence of inaccuracies.
INACCURACY: An alteration to information in a component or system that eliminates, conceals, or corrupts information about the music.
NEUTRALITY: The degree of absence of coloration within a component or system.
COLORATION: An inaccuracy audible as a non-random sonic signature.
RESOLUTION: The absolute limit of information about the music that a component or system can present.
These concepts form some of the basic units of a set of equations that express the relations among accuracy, neutrality, and resolution:
1. CA = (1/L+N+D)
2. CN = (1/DoC)
3. CR = CA + FR
4. SA = SoCA
5. SN = SoCN
6. SR = SA + FR
Where…
CA = Component Accuracy
CN = Component Neutrality
CR = Component Resolution
SA = System Accuracy
SN = System Neutrality
SR = System Resolution
FR = Format Resolution
L = Loss
N = Noise
D = Distortion
So = “Sum of”
Do = “Degree of”
Taking them one at a time…
1. CA = (1/L+N+D). A COMPONENT’S ACCURACY is determined by the amount of loss, noise, and distortion within the component. More specifically, a component's accuracy is INVERSELY PROPORTIONAL to its loss, noise, and distortion. The other way of saying the same thing: A component's inaccuracy is DIRECTLY PROPORTIONAL to its loss (the elimination of information), noise (the concealment of information), and distortion (the corruption of information).
2. CN = (1/DoC). A COMPONENT’S NEUTRALITY is determined by its degree of coloration. More specifically, a component's neutrality is INVERSELY PROPORTIONAL to its degree of coloration. This equation was proposed by Cbw in an earlier post.
3. CR = CA + FR. A COMPONENT’S RESOLUTION is determined by the accuracy of the component and the format resolution of the source. Specifically, a component's resolution is DIRECTLY PROPORTIONAL to its accuracy and the format resolution.
4. SA = SoCA. A SYSTEM’S ACCURACY is determined by the sum of its components’ accuracy. Specifically, they are DIRECTLY PROPORTIONAL.
5. SN = SoCN. A SYSTEM’S NEUTRALITY is determined by the sum of its components’ neutrality. Specifically, they are DIRECTLY PROPORTIONAL.
6. SR = SA + FR. A SYSTEM’S RESOLUTION is determined by the system's accuracy and the format resolution of the source. Specifically, a system's resolution is DIRECTLY PROPORTIONAL to its accuracy and the format resolution.
I'm not really proposing a deep mathematical relationship among these concepts. The equations are more of a mathematical analogy for describing the logical and conceptual relations among these categories.
Cbw – I have given some thought to your suggestions for revising the working definition of ‘inaccuracy.’ Here is what I came up with:
INACCURACY: An alteration to information in a component or system that eliminates, conceals, or corrupts information about the music.
Defining 'inaccuracy' in this way raises the question: How does this new concept of 'inaccuracy' relate to the concepts of 'accuracy,' 'neutrality,' and ‘resolution’? I would like to offer a new proposal about the relations among these concepts. To begin with some definitions:
ACCURACY: 1. The relative amount of information about the music presented by a component or system, comparing output to input. 2. The degree of absence of inaccuracies.
INACCURACY: An alteration to information in a component or system that eliminates, conceals, or corrupts information about the music.
NEUTRALITY: The degree of absence of coloration within a component or system.
COLORATION: An inaccuracy audible as a non-random sonic signature.
RESOLUTION: The absolute limit of information about the music that a component or system can present.
These concepts form some of the basic units of a set of equations that express the relations among accuracy, neutrality, and resolution:
1. CA = (1/L+N+D)
2. CN = (1/DoC)
3. CR = CA + FR
4. SA = SoCA
5. SN = SoCN
6. SR = SA + FR
Where…
CA = Component Accuracy
CN = Component Neutrality
CR = Component Resolution
SA = System Accuracy
SN = System Neutrality
SR = System Resolution
FR = Format Resolution
L = Loss
N = Noise
D = Distortion
So = “Sum of”
Do = “Degree of”
Taking them one at a time…
1. CA = (1/L+N+D). A COMPONENT’S ACCURACY is determined by the amount of loss, noise, and distortion within the component. More specifically, a component's accuracy is INVERSELY PROPORTIONAL to its loss, noise, and distortion. The other way of saying the same thing: A component's inaccuracy is DIRECTLY PROPORTIONAL to its loss (the elimination of information), noise (the concealment of information), and distortion (the corruption of information).
2. CN = (1/DoC). A COMPONENT’S NEUTRALITY is determined by its degree of coloration. More specifically, a component's neutrality is INVERSELY PROPORTIONAL to its degree of coloration. This equation was proposed by Cbw in an earlier post.
3. CR = CA + FR. A COMPONENT’S RESOLUTION is determined by the accuracy of the component and the format resolution of the source. Specifically, a component's resolution is DIRECTLY PROPORTIONAL to its accuracy and the format resolution.
4. SA = SoCA. A SYSTEM’S ACCURACY is determined by the sum of its components’ accuracy. Specifically, they are DIRECTLY PROPORTIONAL.
5. SN = SoCN. A SYSTEM’S NEUTRALITY is determined by the sum of its components’ neutrality. Specifically, they are DIRECTLY PROPORTIONAL.
6. SR = SA + FR. A SYSTEM’S RESOLUTION is determined by the system's accuracy and the format resolution of the source. Specifically, a system's resolution is DIRECTLY PROPORTIONAL to its accuracy and the format resolution.
I'm not really proposing a deep mathematical relationship among these concepts. The equations are more of a mathematical analogy for describing the logical and conceptual relations among these categories.