[Jun8]

Looks great! One question:

"This is known as an Octave and is not considered a new note. An Octave is the same note with a higher pitch."

Why is this so? I guess I'm totally tone deaf since I get no understanding of the sameness of notes separated by one octave by listening to them. In the same vain the good sound/bad sound example that opens the harmony section sound both good to me.

[phormula]

The notes that sound good together have a basis in the harmonic series, the 1st and 3rd are octaves of the fundamental, 2x an 3x the frequency. the 2nd harmonic and 4th harmonic make up the other 2 notes in a major chord. Periodic sounds that are not pure sine waves (like vibrating strings) have harmonics. Our ears are attuned to hear these harmonics and this natural phenomenon is the basis of all pitch, melody and harmony in music.

https://en.wikipedia.org/wiki/Harmonic_series_(music)

[fenomas]

If you want the first-principles answer, it is that sounds in nature tend to occur as multiple overlapping tones one or more octaves apart, so our ears and brains have evolved to hear a sameness in them.

That is, when you pluck a guitar string that's tuned to 400hz, it also vibrates at 800hz, 1600hz, and so on. (Do an image search on "guitar string harmonics" if it's not obvious how that would work.) But we hear such overlapping tones as a single "note", whereas a 400hz tone overlapping with a 600hz tone sounds like a chord.

[tiglionabbit]

For the octave, if you heard them at the same time they would be a bit harder to distinguish than most other ratios, so it would be nice if the example let you do that.

And yeah, the "bad" example is not really very bad. It's a little bit tense, but there are much worse ratios they could have chosen.

[nandemo]

Agreed. Saying they're the "same note" is an oversimplification. They're "equivalent" in certain contexts, which is an important distinction.

They aren't the same note: if someone plays A3 (fundamental is 220Hz) and then A4 (440Hz) you can easily tell them apart! In contrast, if they play 220Hz and then 221Hz an untrained listener will most likely hear them as the same note.

In some contexts a note and its octave can be thought of as equivalent: if you are playing a chord you can often replace A3 with A4 (and vice-versa) without changing the chord's feel and function. However, that isn't always true. For example, playing G#3 and A3 at the same time will sound more dissonant than playing G#3 and A4 (a minor 2nd is more dissonant than a minor 9th).

[wyldfire]

IIRC octaves are what's referred to as harmonic frequencies in physics/kinematics/etc. "Why is it the same note?" AFAIK it's because the higher ones are multiples of the base freq.

But TBH I know next to nothing about music so I could be off.

[rspeer]

Close. Each shift of an octave doubles the frequency, so octaves are specifically harmonics that are powers of 2. Other harmonic ratios make other intervals (including intervals that aren't in our scale, when you get to bigger prime numbers).

Most instruments produce harmonic multiples of the base frequency. (Percussion instruments don't.) So if you play a note at 110 Hz, there are also pitches at 220 Hz, 330 Hz, 440 Hz, etc. contained inside it. If you play a note an octave up, at 220 Hz, it contains pitches at 220 Hz, 440 Hz, 660 Hz... which is similar enough that it sounds like "the same note".

(This doesn't explain why 330, 660, 990, ... sounds like a different note, though. Maybe it doesn't to an untrained ear.)

[dharma1]

I haven't tested this, but my intuition is that any musical sound with harmonic (as opposed to inharmonic) partials will sound like a single note, if the first fundamental is clearly the loudest, and the harmonics follow some kind of natural distribution in terms of loudness and temporal decay.

Two notes played in an octave would be quite distinct since you have a clear first fundamental for both notes, and the loudness/decay of the harmonics is slightly different between both notes