BARRY'S 8 TRACK REPAIR
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In this section, I'll show you how manufacturers can rate a 70 watt amp at 200 watts and get away with it.
Unfortunately for the uneducated buyer, there is more than one way to rate power output.  The more reputable
manufacturers use honest techniques, but some of the cheaper makers inflate the figures (legally) to help sell
more products.  Here are a few ways in which they can do that.  First, a very brief description of an audio wave.

A typical audio wave is ALTERNATING CURRENT - the same type of current you get from a wall outlet, but usually
of a much lower voltage and at frequencies which are continuously changing, rather than the straight 60 cycles
per second found at the outlet.  For instance, bass notes are in the 30 - 200 range, voices and guitars cover
roughly the 300 - 3000 range, with drum cymbals and "harmonics" (the characteristic of sound that gives each
instrument and voice its particular flavor) going up as high as 18,000 cycles per second.

A wave of 60 cycle ALTERNATING CURRENT from the 110 volt wall outlet swings from NEGATIVE 55 volts - to zero
volts - to POSITIVE 55 volts - 60 times per second.  The swing from -55 volts to +55 volts is how we end up with 110
volts when all is said and done.   Audio waves, in a very general sense, behave in the same manner.

Now let's take an actual audio wave and see how it can be rated 3 different ways. As a quick aid to visualization,
I've placed horizontal cursor lines on the scope.  All 3 photos are of the exact same wave, with the cursors
placed according to how we will measure the output power (or in this case, voltage - but we'll pretend that
the readout is in watts for simplification).  All 3 waves are 200 "watts" from the negative to the positive peak,
with both positive and negative peaks 100 watts away from the zero reference line (bottom cursor):
Deceptive Power Ratings
This picture shows the measurement being taken
from the ZERO REFERENCE to about 70% of the positive
peak.  This is called the "average" power level, since
full power only occurs at the very tops and bottoms of
the peaks, and is realistically the amount of power the
amplifier can safely deliver for extended periods of
time.  That's why it is also called "continuous" power
or, more technically, "RMS" power.  The RMS stands for
Root-Mean-Square and is a mathematical expression
we needn't go into here.  Bottom line of this lesson:
THIS AMP PUTS OUT 70 WATTS RMS

RMS IS THE HONEST WAY TO REPRESENT POWER
Here is the exact same wave, except this time we are
measuring it from the zero reference to the top of the peak.
As you can see, 70 watts RMS suddenly becomes 100
watts "peak"  This is the most common way to represent
power output these days, especially among cheaper
manufacturers.  As most consumers are not educated
in the technical end of audio, using this power rating
makes the amplifier APPEAR more powerful.  If the specs
on the unit say simply "100 watts" without the "RMS"
after it, it usually means it is rated in PEAK power.  BUT,
it is still only 70 watts of true, honest power.

"PEAK" POWER RATINGS ARE DECEPTIVE!
Now it gets even worse, because we're measuring the
SAME WAVE from top peak to bottom peak.  VIOLA -
Our 70 watt amplifier instantly becomes 200 WATTS!
This, unfortunately, is also often used to rate amplifiers
in a misleading way.  To make it even worse, they never
say "peak to peak", only "peak".  This amplifier cannot
deliver more than 70 REAL watts for any length of time!
The worst rating ever is called I.P.P. which stands for
INSTANTANEOUS PEAK POWER and means the amplifier
will deliver "1000 watts" for a split second before it blows!

DON'T JUST LOOK AT THE NUMBERS!
Reputable manufacturers will state the power rating method after the numbers,
such as "100 watts RMS per channel", and many will even include the frequency
response and distortion factor.  REMEMBER that an amplifier which simply says
"1000 watts" could actually mean 70 REAL, HONEST watts for both channels combined!
Distortion levels above 2% can be heard by a discriminating ear, as well as limited
frequency response.  The human hearing range is roughly 20 Hz to 18,000 Hz.  An amp
(or speaker) that only goes down to 50 Hz will have poor bass, and anything below
about 15,000 Hz on the high end will sound dull and muddy.  Be careful, and check
the manufacturer's specs on any piece of equipment you plan to purchase.

Reliable and ethical specs (example):

100 watts RMS per channel from 20 to 20kHz with no more than 1% total harmonic distortion

Misleading and deceptive specs:

300 watts "peak" power - when you see the word "peak", cut it in half to get REAL power,
and note whether it is per channel, or for both channels combined.  If the distortion
factor is not mentioned (also called THD), it's probably for a reason!
The human ear - an imperfect device

No matter how sharp your hearing is, it is far from accurate in most cases.  For instance, the ear has a
LOGARITHMIC, rather than linear, response to changing volume levels.  Put simply, it takes 10 TIMES the audio
power to equal TWICE THE APPARENT VOLUME.  Thus, if you have a 100 watt stereo and want twice the loudness,
you need to upgrade to 1000 watts.  For most people, it takes TWICE THE POWER to make it barely louder, so
upgrading to a 200 watt stereo might lead to disappointment.

Ever listen to a song that starts with the bass guitar?  Chances are, when the rest of the band comes in, they
sound out of key for a few moments.  That is because the ear doesn't perceive PITCH properly either, at least
not at the extreme low and high ends of the frequency spectrum.  Very low notes appear higher, and very high
notes appear lower in pitch.  So when you hear that bass solo, it's not the band that is off key - it's your ear!

Piano tuners compensate for the ear's inaccuracy by lowering the bass tones and raising
the high notes.  This process is called "Stretching the octaves".  As this is a subjective
phenomenon and not an exact science, different tuners tune them differently - sometimes
at the individual discretion of the pianist!
Other interesting facts about sound

1.  Sound travels slower at higher altitudes.  The speed of sound at sea level is approximately
1130 feet per second; at 10,000 feet it is only about 980 feet per second.

2.  Sound travels faster through solid materials than through air - MUCH faster!  For example,
sound travels at about 4800 fps through water, and about 10,000 fps through glass.

3.  Sound intensity (loudness) is on a logarithmic scale.  A rock band produces sound levels
MILLIONS OF TIMES GREATER than normal conversation, or even a sharp hammer blow.

4.  Music (at least fundamental tones) are but a tiny portion of the audible spectrum.  The
highest note on the piano is only 4186 Hz, yet we can hear up to about 18,000 Hz.  However,
it is the presence of harmonics (also called overtones) that occupies the remainder of the
spectrum.  The presence and absence of overtones is what gives each instrument and
voice its particular "sound".  If not for overtones, a piano would sound very similar to a
guitar, and music would be pretty boring.  Comparing the sound of AM radio to FM offers
a good demonstration of the increased overtone content of FM, even though you can hear
all musical notes on AM radio.  Overtones give music its brilliance and crispness.

5.  The human ear does not perceive all frequencies equally at lower volume levels.  The
extreme low and high ends of the spectrum drop off at lower levels, and some older stereo
equipment has a button called "Loudness" to compensate for this.  NOTE:  It's best to turn
this feature OFF at high volume, or you'll get too much bass.

6.  Bass is nondirectional; this means you'll hear it no matter how the speakers are placed.
Highs, on the other hand, are quite directional and depend heavily on speaker placement.
This is why many subwoofers are designed to direct their thrust downward; then they can
even use the floor as a vibrating medium - sort of like a huge soundboard.  If you play the
bass guitar, you can often actually hear yourself better farther away from your speakers.
This also explains why the modern-day "thump thump" from cars is so objectionable to
everyone else except the driver!  The driver can hear it less than you do.
Our musical scale

You'd never know it, but the development of our modern scale, i.e., determining the exact frequencies of all
notes used in music, is a huge compromise.  Back in the candlelight days, music was constructed using
mathematical formulae and sounded sweeter and smoother - at least in half the keys.  In the other half of the
keys, it sounded horrible.  Obviously, composers could not limit their compositions to a certain number of keys;
even music written in the "good" keys still needed the freedom to modulate to any other key in order to keep
writing original stuff, and to offer the millions of flavors and textures we find in music today.

So, around the time of Bach, it was decided to divide the 12 tones (from A to G#) into equal segments, with
any two adjacent tones being the same "distance" apart from any other two adjacent tones.  This violated
the mathematical ideals and indeed results in music that is just slightly out of tune (yes, every piece of music
we hear), but the tradeoff was acceptable intonation in all keys, and new worlds for freedom and expression.

If you play the first 2 notes of "When the Saints Come Marching In" together (the "Oh when" part), you can
hear harmonic "beats" - the sound repeatedly gets louder and softer several times per second.  This is
called "dissonance".  Now, that second note used to be a bit higher and was perfectly in tune with the first
note.  That second note was called a "mathematical third" or, more specifically, a "Pythagorian third" after
the Egyptian mathematician.  Unfortunately, only half the keys could share this perfection.

One reason that the violin, the pedal steel guitar and the human voice can sound so sweet is this:  without
built in frets, stops or fixed pitches that can't be adjusted, these instruments can actually "get in there" and
play Pythagorian thirds, perfect fifths, etc.  In fact, while the keys of F sharp and G flat are musically the exact
same keys on the piano and most other instruments, they are interpreted and played differently on the violin!
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