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I never learned any music. My only understanding of music came from the physics labs at school, messing around with signal generators. My wife was trained in pi

I never learned any music. My only understanding of music came from the physics labs at school, messing around with signal generators. My wife was trained in piano, I've asked her countless times, so what frequency are you playing when you hit this key? Why is this key, called middle C, yet C repeats further down the keyboard? Doesn't a C map to a unique frequency? I've been asking her for a translation of music into physical terms for years -- to no avail (she's a doctor). I'm looking for a "for dummies" type book, but instead, it would be "Music for Engineers with no music background." Also why are there pure C notes and C chords... I want that book!

ryansouza 9y ago
Here you go: http://tobyrush.com/theorypages/index.html http://tobyrush.com/theorypages/index.html
8bitsrule 9y ago
In most Western music there are 12 tones in an octave. So if you play a note with a fundamental frequency of 440 Hz, it will repeat itself (one octave higher) 12 steps later at 880 Hz. Notes one or more octaves apart all have the same name! Diving deeper: a 'C' on a piano is actually made up of -multiple- frequencies. The 'same' 'C' on any other instrument is made up of a -different- set of frequencies. See: overtones.
kaoD 9y ago
About that specific question, the term you're looking for is "pitch class".
TheOtherHobbes 9y ago
It's called Middle C because it's the C in the middle of the keyboard. All the other Cs are called C because we perceive them as "the same note." Ask her to play a tune, and then play it again an octave higher and then lower. The pitch is different, but there's also a sense that all three versions are the same. Mathematically, pitch is like a helix. Points with the same rotation - which happen to be a frequency ratio of powers of 2 - sound very closely related. Instead of giving every single note a different name, it's useful to give notes the same repeating set of 12 names and then add a separate "height" variable - called the octave - to describe which turn of the helix they're on. If you play pitches with the same rotation at the same time they blend well together. In fact you can barely tell them apart. Of course you can rotate by less than a full circle. If you play the same tune with a different pitch offset - say one note instead of twelve, which is the smallest rotation you can do on a conventional keyboard - you'll hear it's still the same shape, but there's a jarring effect between the different versions. Some rotations sound good together, but not as good as the identity rotation. Others clash and sound bad. As a guide, simple divisions of the pitch circle - like 3:2 - sound smoother than the more complicated divisions. The twelve notes approximate the rotations that sound best together. You get a good mix of smooth and not so smooth blends, and you can build all kinds of combinations with them. You use approximations and not exact whole number ratios because you want to be able to write music that isn't stuck with a single starting/reference note. You can play the same tune at different starting pitches and the relationships between the notes doesn't change. If you use whole number ratios a tune that sounds good starting on one note sounds weird and sour starting on others. The pitch spiral turns into an oval corkscrew, and the neat rotations get distorted. And yes, all the As, Bs, Cs have their own specific frequencies. By convention A = 440Hz, and everything else is tuned around that. All the As are powers of 2 either side of 440Hz - from 27.5Hz, which is the lowest note on a piano, to 3520Hz for the highest A.
- lighttower 9y ago
  Wow. Thank you for this! Your writing here is making clear what's been the issue. Music people don't speak Hz, they have their own specific terms that I can't parse because they layer many physical concepts.
  - lamename 9y ago
    So true. Communication often breaks down when people who think or speak at different levels of abstraction meet, and their backgrounds collide. Worst case: they argue in vain. Best case: the above happens

ryansouza 9y ago

Here you go: http://tobyrush.com/theorypages/index.html http://tobyrush.com/theorypages/index.html

8bitsrule 9y ago

In most Western music there are 12 tones in an octave. So if you play a note with a fundamental frequency of 440 Hz, it will repeat itself (one octave higher) 12 steps later at 880 Hz. Notes one or more octaves apart all have the same name! Diving deeper: a 'C' on a piano is actually made up of -multiple- frequencies. The 'same' 'C' on any other instrument is made up of a -different- set of frequencies. See: overtones.

kaoD 9y ago

About that specific question, the term you're looking for is "pitch class".

TheOtherHobbes 9y ago

It's called Middle C because it's the C in the middle of the keyboard. All the other Cs are called C because we perceive them as "the same note." Ask her to play a tune, and then play it again an octave higher and then lower. The pitch is different, but there's also a sense that all three versions are the same. Mathematically, pitch is like a helix. Points with the same rotation - which happen to be a frequency ratio of powers of 2 - sound very closely related. Instead of giving every single note a different name, it's useful to give notes the same repeating set of 12 names and then add a separate "height" variable - called the octave - to describe which turn of the helix they're on. If you play pitches with the same rotation at the same time they blend well together. In fact you can barely tell them apart. Of course you can rotate by less than a full circle. If you play the same tune with a different pitch offset - say one note instead of twelve, which is the smallest rotation you can do on a conventional keyboard - you'll hear it's still the same shape, but there's a jarring effect between the different versions. Some rotations sound good together, but not as good as the identity rotation. Others clash and sound bad. As a guide, simple divisions of the pitch circle - like 3:2 - sound smoother than the more complicated divisions. The twelve notes approximate the rotations that sound best together. You get a good mix of smooth and not so smooth blends, and you can build all kinds of combinations with them. You use approximations and not exact whole number ratios because you want to be able to write music that isn't stuck with a single starting/reference note. You can play the same tune at different starting pitches and the relationships between the notes doesn't change. If you use whole number ratios a tune that sounds good starting on one note sounds weird and sour starting on others. The pitch spiral turns into an oval corkscrew, and the neat rotations get distorted. And yes, all the As, Bs, Cs have their own specific frequencies. By convention A = 440Hz, and everything else is tuned around that. All the As are powers of 2 either side of 440Hz - from 27.5Hz, which is the lowest note on a piano, to 3520Hz for the highest A.

lighttower 9y ago
Wow. Thank you for this! Your writing here is making clear what's been the issue. Music people don't speak Hz, they have their own specific terms that I can't parse because they layer many physical concepts.
- lamename 9y ago
  So true. Communication often breaks down when people who think or speak at different levels of abstraction meet, and their backgrounds collide. Worst case: they argue in vain. Best case: the above happens