Piano Generator

In frequency terms, not musical ones, an octave is a pair of frequencies where the upper frequency of the pair is two times the frequency of the lower frequency of the pair. Examples would be {256 Hz, 512 Hz}, or {440 Hz., 880 Hz.}. The absolute values of the frequencies in the pair do not matter -- only the ratio. As you can see there are an infinite number of octaves.

Given an octave we can subdivide ANY octave in to 12 even tempered (equally spaced) parts on a logarithmic scale. We do this by making the ratio between adjacent parts equal to the 12th root of 2. That is the 12th root of 2 ≈ 1.05946. Taking 440 Hz. as the beginning of an octave the next step would be 440 * 1.05946 ≈ 446.164 Hz. That resulting smallest interval, 1⁄12 the width of an octave, is called a semitone or half step. Note that we are generating the steps by using a constant to multiply the previous result. This means the semitones or half steps will never be the same size on a linear scale, but the ratio of each pair of adjacent semitones will always be the 12th root of 2.

That is a start at a non-musical explanation, which can be found here:

Ascending notes (semitones) are each a multiplication of the frequency below, with a factor of 12th root of 2.
So, 12 successive increments (multiplications) gives a doubling of frequency; one octave.

For historical reasons, of the twelve notes in each octave, only seven have direct letter names, matching the white notes on a music keyboard.

The unnamed inbetween ones (black keys) are called the sharp of the lower named note they are next to, equally the flat of the next higher named note...

The octaves have the same set of A-G notes, with each specific octave identified by a by a suffix number.

Such as a guitar has all sequential notes (semitones) as individual frets, within the range of each string.

Thanks Papabravo, ....that's quite a headache. Was it set up that way, because of our hearing response? So the octave is the fundamental and the 2nd harmonic. With 12 log steps semi tones between. And any F can be the fundamental. What do the peddles do?

Thanks rjenkinsgb, for the explanation of the white and black keys. and sharp and flat, depending on going up and going down.

So the doe, ray, me, etc, is the semitones? But with probably different spellings. French maybe or Latin?

Now I kinda wish I had a keyboard, to listen closely to the difference.

I think that music is wonderful. I think that RAP is not music, it is a guy reading a book out loud with a drum in the background. I do not like the severe distortion in most acid rock "music".

Frequently I think about the musical notes, rhythm and harmony of a piece of music. I can whistle it, hum it or poorly sing it.

I laugh when I hear (very frequently lately) someone singing or RAPping with "autotune" correcting their pitch.

Thanks all, for the clearer understanding. And all musical instruments would follow this scheme. Are the guitar strings, and even other instruments, adjusted with 1/12 length adjustments? Or 1/24th adjustments?

What do those piano pedals do?

Yes it seems our high tech can make anybody a rock star. Maybe in the future our tech will allow any to become a sports star. Maybe even brain implants to make doctors.......who knows? I think Musk is working on some kind a brain interface. Probably others too.

BR-549 said:

... So the octave is the fundamental and the 2nd harmonic. ...

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Yes, and an octave can start at any frequency, and the 2nd harmonic is twice the fundamental.

BR-549 said:

So the doe, ray, me, etc, is the semitones? But with probably different spellings. French maybe or Latin?

Click to expand...

Those are the seven named (white) notes, which can have either one or two semitones between them & the end "do" an octave higher than the starting one.

BR-549 said:

Thanks all, for the clearer understanding. And all musical instruments would follow this scheme. Are the guitar strings, and even other instruments, adjusted with 1/12 length adjustments? Or 1/24th adjustments?

Click to expand...

Some countries & traditions have other intervals and numbers of notes, but the equal increment 12 semitone one is the commonist in western music - and the nearest to being logical!

Guitars use all twelve semitones with no distinctions, one fret per semitone.
It's down to the tuning of each string as to what the lowest note each can play is.

The commonest tuning has each higher string starting five (or four) semitones higher, a 5-5-5-4-5 pattern, so the high string on a six string guitar is then two octaves, 24 semitones, higher than the low string.

You can see the progressive logarithmic intervals in the spacings of the frets, wide near the head of the neck and narrow at the body end:

BR-549 said:

What do those piano pedals do?

Click to expand...

One is sustain. Each key mechanism normally has a felt pad pressed against the strings it sounds, to mute them, & that lifts when the key is pressed, so the note stops when you release the key.

The sustain pedal lifts all the damper pads so notes are not ended when the keys are released.


Each piano key has up to three strings side by side in the piano frame, normally all struck at the same time by the key mechanism hammer when a key is pressed.

One of the other pedals shifts the entire mechanism sideways slightly so the key hammers only strike one string rather than all.

The third pedal is a variant of the sustain, but only locking the damper pads on keys that are already pressed when the pedal is pressed; those notes are sustained until the pedal is released, while all others still mute when released.

I had no idea about those pedals. Thanks for that. So one key strikes 3 strings in the piano?

I could not follow your guitar strings. Just use one string. Does a fret, change to one semitone?

And the taut on the string changes wavelength, right? That would interfere with the fret spacing, wouldn't it? A horn would change tube lengths for notes and could be set. But with a string, can the wavelength be changed with taut? Or tension?

Hold on a second, I just got it. We match the frequency to the SET length with taut. And the other fundamentals are set to that same length......and the fret distance remains set.

That's really neat.

Here is a piano for you to play with. https://www.onlinepianist.com/virtual-piano
Click "Letter Notes" at the top to show the A-G letters on the keys.

But each instrument, even when playing the same note, has different overtones that are part of it's waveform. Here are a few. https://www.researchgate.net/figure...ents-at-a-particular-frequency_fig1_305333971
That is why they each sound different.

Lots more waveforms can be found by searching "waveforms of different instruments"

Thank you all very much. I am quite satisfied with all the comments and the idea of frequency related with music. That's all I need for now.

Fantastic!. I haven't been near a piano for maybe 69 years and I can still play a few songs I learned when I was 8 years old. Thanks for the link to the Virtual Piano.