Well, this takes me back.
Let's see, it's been awhile.

1- Magnetism exists in 360 degrees. Think of any magnet. There is no 'line' of magnetism, it exists all around
So think of a length of tape as if it's a magnet. the magnetism exists along the length of the tape as well as all around the tape. This presents a problem when you start winding tape onto a reel where all the layers are in contact with each other and their magnetic fields as well.
2- Corrective System in this case is referring to something that can change the dynamics of the 'program' (see #3) like compression or noise reduction.
3- Program = Source. (the thing you are recording)
4- yes
5-6 - They're saying (although perhaps not too clearly) that tape doesn't have a linear transfer across the entire dynamic range. (It seems they left that bit out) The highest levels will oversaturate the tape which is known as tape compression. Lowest levels will disappear into the tape hiss. Only the mid level will transfer more accurately.
Tape only has about a 70db dynamic range.

I think that's the way I remember it.

Ah I see, few more questions if you have a chance!

(A)So the program they're referring to is the audio signal that's being received?
(B)The tape does not have a linear transfer characteristic because when the tape is wound up by the tape machine, the tape ends up being wound over itself in layers, and thus the magnetic field present on it interferes with the layers above and below it? Or is it because at different angles/degrees, magnetically speaking, it would have a different magnetic strength? Or is it because the magnetic field surrounding the tape fluctuates? Or is it because the current being applied to the record head might be fluctuating? (does said current fluctuate?)
(C)referring to number 2's answer, the corrective system of compression for instance, would it be pre or post recording? meaning would it be applied to the source signal prior to it reaching the tape machine, thus correcting the source, or post the record tape head, thus correcting the recording itself? (If that makes sense? sorry probably not well worded on my part!)

Thanks for your help been stressing out about this throughout the whole chapter!

I'm sure one of our esteemed colleagues 'Remy' will be along shortly to give you more info than you wanted.
In the mean time.....

A - Yes, Program AKA Source AKA Talent AKA 'The Band' AKA sound AKA input.

B - Well at some point I'm sure that magic must take over because the more you think about this stuff the more it just seems slightly beyond normal reasoning that this method can capture even the slightest sound much less reproduce it faithfully.
But without getting too far ahead of ourselves and keeping to the paragraph you provided- They're talking about tape capturing levels.
This is not linear across the entire dynamic range. I think we can replace the word linear with "accurate" in this case.
The thing about the winds of tape is that one layer of tape will impart a little of it's magnetic signal on the wind of tape next to it.
So the purity of recording is compromised. It's one of life's little 'Deal with it' situations. Then there's the retention quality of the tape itself.
All these things work toward deteriorating the pristine signal (program) that you were trying to capture.
(really, it's hard to believe we actually recorded this way - much less make hit records)
The other points you bring up also have an effect, but I don't want to get off on too many tangents. This stuff can give you brain a hernia.
The short of it is, that if tape only has a dynamic range of 70db. and if your source (program) is greater than that, then you're going to have a problem.
You either have to record at a lower level so as to not distort the recording but you'll lose the softest sounds.
Or record at a higher level to capture the soft stuff, and risk tape distortion at the higher levels.
Or insert something into the signal chain to handle the softest and loudest sections.
THis will allow you to have the softest and loudest things on tape, but it won't be 'accurate'

C - Pre Recording. In the case of something like noise reduction. The sound is encoded (processed) pre recording, then on play back it is decoded to remove the hiss (probably more magic)

Ok now it makes more sense. Thanks a lot for the help! about 300 other points in the chapter have finally clicked haha

Yes, don't take the word 'linear' too literally. If I were to paraphrase all the hooey:

Studying the traits of magnetic tape recording is made more complex by the fact that tape does not always have consistent recording/playback characteristics.

Without any corrective system, tape recordings of music/sound with a wide dynamic range will not accurately reproduce the very quiet or very loud portions of the recording. The quieter and louder parts of the recording will suffer non-linear compression. Only the material recorded at nominal levels will be reproduced with a high degree of accuracy.

Now that we've got that behind us -
[ I don't necessarily agree that low level program suffers from compression. Recording at very low levels leads to poor signal to noise, but I don't believe it gets compressed in the conventional sense. And in the hands of a zen master - analog tape compression/saturation can be a beautiful thing ]

In response to your post dvdhawk, I see what you mean, the tape just isn't going to hold it's properties in a consistent manner if it's magnetic field is being interfered with by other parts of the tape's different magnetic field.
I do have some questions though.
The signal to noise ratio you mentioned would definitely be a problem, wouldn't tape hiss and the general noise from analog gear tend to sit at a relatively consistent level in relation to the signal coming in? As you push the levels so this noise will rise but not as much as the signal itself? Am I correct in this assumption?
If so, wouldn't using single-ended and/or double-end noise reduction systems, for example a Dolby SR system and a noise gate (is it possible to use both systems?), tend to reduce the chances of having to push the gain so high that said tape compression/saturation occurs?

I would agree that the noise-floor inherent in the tape itself would remain constant - but independent of the record level. I don't believe the tape hiss changes with level. Different tape formulas would have different sonic qualities and self-noise. The self-noise is masked and becomes less noticeable (or completely unnoticeable) when the signal rises to a certain level.

Since you're so young you may never have the chance to experience the joys of analog tape. And I'm a little concerned that as you read words like 'hiss', 'distortion', and 'noise' you might imagine that recordings prior to the digital-age were pure garbage. Just so you don't get the wrong idea about analog, the signal-to-noise ratio on a professional machine is more than tolerable, it could be downright great. A high-quality tape - recorded and played back on a well-aligned and maintained machine can sound absolutely stunning. It had a natural warmth and character that no one has found a way to synthesize in a DAW.

The speed the tape is running makes a HUGE difference in the quality of the recording. Consumer cassette decks ran at 1 7/8 inches of tape per second passing over the heads, consequently they sounded relatively low-fi. Intermediate level machines typically running 3 3/4 or 7 1/2 ips sounded significantly better. And studio-quality reel to reel machines running at 15 ips or even 30 ips - wow! Running tape at higher speeds yielded much better recordings. But, doubling the speed cuts the recording time in half due to the physical limits of reel size and length of the tape. Frequency response and signal-to-noise ratio got dramatically better at high speeds. But as you would imagine, it gets pretty expensive for those big studios using 2" tape. [ there was a time you had to be talented to get a record deal, simply because the company was investing a fair chunk of money into tape as well as studio-time ]

The modern-day equivalent to tape speed would be sample rate. (how much audio information are we processing every second)

At 15 ips or 30 ips, very little noise-reduction would have been necessary. Dolby was a necessary evil in some cases and while it could reduce tape-hiss significantly - I always felt like it killed too much of the treble content in the process on my relatively cheap gear. A lot of people would record with the Dolby on, and playback with it switched off.

I'm far from an expert on the pro-level tape decks, so if we're lucky Ms. Remy (or others who could circle the earth with the miles of tapes they have used) will be along eventually to school us all on this lost art.

Don't worry I do know the legend that was analog recording. Tape is to recording as vinyl is to djing. It gave that extra bit of warmth and depth that DAW's/CD's just can't reproduce. Make no mistake I know that with current advances in technology we're getting slowly closer to that level of quality, but i'm sure it could be a while till we can replicate that sound, if ever, using a DAW.
Also, as I was reading that part you mentioned about the speed of tape I was comparing it to sample rate, so I think I understand where you're coming from.
As far as I know there tends to be a trend towards attempting to replicate that old-school analog sound either through hardware or plug-ins, and this is evident purely in the fact that a band has recently requested one of our lecturers to record their album onto tape, and my college happens to have a 100% working tape machine and the ability to record onto tape. Not exactly a common item in South Africa I might add.
There's also a trend as far as I've picked up of various studios tending to aim at acquiring old-school compressors, limiters, VU meters, etc. Am I correct?
Something involving valves & tubes & compressors? I know that sounds bad, and uneducated, but i'm rather stressed and can't think how to explain what I mean by that.
Thanks to both of you again, I'm onto the effects & effects processors section now, the idea of creating multi-tap delay lines on tape using multiple playback heads is quite interesting for someone who has never had the privilege of working with tape. Whether anyone would like to admit it or not, to work on magnetic tape of high quality required a lot of skill. Almost anyone can click on a record button, doesn't mean it'll sound good, but you know what I mean. To record on tape however was not so easy as I've discovered!
Last thing, I spent a good year and a half only using plug-ins when it came to my production, etc. Since going to my college and having access to hardware, my whole mentality about plug-ins has changed. Plug-ins are useful and all, but there's nothing like actual analog hardware!

In relation to the quality thing I mentioned at the beginning of my last post, am I right in assuming that the quality of tape recordings is higher than that of the sound cards and DAW's out at the moment?

You're starting to get into a topic that's both subjective and controversial.
We'll tread carefully.

A Proaudio Daw is technically superior in quality. Playback will be closer to the source than when you play back tape.
We have a good 30+ years of history listening to High quality analog tape. We're used to it, with whatever flaws and happy accidents it provides.
We only have about a good 10-15 year history with the modern DAW.
You might liken it to today's hi quality cameras. It captures it all. Seemingly even more than what we see with our own eyes. Then we go back in and airbrush it to make it look more 'natural'.

Got some new questions, different topic now, Effects and Effects processors.
Firstly-I understand flanging and chorus effects to be created using delay lines? They are similar effects?
Secondly-Vibrato. Type of Flanging or is it it's own effect like chorus is?
Thirdly-Phasing. In terms of effects, is Phasing a type of flanging or is flanging a type of phasing? Also, is Phasing it's own effect like Chorus is?

Sorry for all the questions, don't really have anywhere else to go at the moment!

OK, this is a gross simplification, but you only have until Thursday. Think of a piece of tapes as a digital system. But instead of 24 bits you have millions and each bit is a magnetic compass needle pointing either up or down. When you start, the needles are randomly up and down with an average of zero. But when you apply a field some of the needles "flip" and line up with the field. (They can't just rotate a little. They have only two choices - up or down.) At a "medium level" field everything is linear - twice as much applied field, twice as many needles needles flip - three times the field, three times as many needles flip. But there are two "nonlinear" regimes. One is a large field - where almost all of the needles are pointing in the same direction. The tape is "saturated" and there is no way to get it to react linearly to the input. The other regime is a very small applied field - one with too little energy to flip any of the needles. The tape doesn't react to the very small changes in the applied field and just stays at zero.