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All the notes in the world!?

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What are all the musical notes and accords that "exists"? It would be better if the notes were described in terms of frequencies. Where can I find such information? Thanks in advance.

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You could get a thesaurus of scales. Has such scales as semi, hemi, and demi tonic scales, with interpolation around different centers. This is still all dealing with a 12 tone system. You an also have scales, tone sets, tuning systems, that have more than 12 notes. Some have 48, some have 16, essentially you can create your own as well.

What you are proposing is something that could be feasible, but couldn't be functional in a non-academic environment. Differentiating the modulation in pitch could be done over a long period of time, a la Penderecki.

Mathematically, you could always approach a pitch but never reach it. The untrained ear can sometimes not even detect pitches that are nearly a half step off.

Google this:

Slonimsky's 'Thesaurus of Scales and Melodic Patterns'

Might help you

Sean Beeson

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Okey, I have another related question.
I dont understand too much notes so I will ask this in frequencies.
Suppose you have two sinus waves with different frequencies, f1 and f2.
Adding them together would create some wave (an acord?)
Now you need to select a third sinus wave, with frequency f3, so that the third wave will sound the closest to the addition of the two first waves.
In the mathemtical approch, this depends on what norm you select to represent distance between waves.
If you choose a norm based on the fourier coefficients of the waves.
By this norm the best way to choose f3 is choosing it to be either f2 or f1, depending who has bigger amplitude.
However, would this f3 wave sound the closest to the addition of f1 and f2 to the human ear?
Or is there another norm that should be considered here?

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Guest Anonymous Poster
when adding two waves (sines) of different frequencies this results in a complex wave where the higher frequency 'rides' the lower frequency (depends a little on the difference of frequency). But the human brain can recognize those two different frequencies from that one wave. When mediating or transforming the complex wave into a nicer sinus, this effect is totally gone and the brain will recognize a new frequency.
An accord consists of different frequencies which match in a sense, they are pleasant to hear simultaneously, but they are not a new frequency. Trying to merge two tones into one will in most cases (if the frequencies differ a lot) result in a totally different tone. Think of pressing one key on a piano simultaneously with the key four to the right. Pressing the key in the middle sounds in no way like those two together.
Hope it helps.

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Quote:
Original post by Anonymous Poster
when adding two waves (sines) of different frequencies this results in a complex wave where the higher frequency 'rides' the lower frequency (depends a little on the difference of frequency). But the human brain can recognize those two different frequencies from that one wave. When mediating or transforming the complex wave into a nicer sinus, this effect is totally gone and the brain will recognize a new frequency.
An accord consists of different frequencies which match in a sense, they are pleasant to hear simultaneously, but they are not a new frequency. Trying to merge two tones into one will in most cases (if the frequencies differ a lot) result in a totally different tone. Think of pressing one key on a piano simultaneously with the key four to the right. Pressing the key in the middle sounds in no way like those two together.
Hope it helps.


I didnt say that f3 is going to sound exactly the same as f1 and f2.
I just asked if there are some f3 that sound closer to f1 and f2 then others.
For instance you can choose f3=f1. Would that sound closer then choosing f3=f2 or f3= (f1+f2)/2?
Or are you saying it doesnt matter which f3 I will choose, they will all sound different?

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if you add two sine waves with the frequencies f1 and f2 you will actually get a wave with the frequency f3 = (f1 + f2)/2 *but* this wave is amplitude modulated by another sine (actually cosine, but that's only a 90° phase difference and irrellevant in this case) wave with a frequency f3b = (f1 - f2)/2 thus if f1 and f2 are close together (ie f3b is low) it will sound like a single tone of the frequency f3 = (f1 + f2) / 2 with a fluctuating volume (beating)*, but if the difference between f1 and f2 (and thus f3b) is large it will sound more like something different, highly dependant on the frequencies chosen. for example if f2 is an integer multiple of f1 it will be part of the natural overtone series of f1 and thus most likely not audible as a separate pitch but as a change in tone/character. but if for example f2 = 2^(1/3) (3rd root of 2) it will sound more like a separate note. (in this case the third, thus forming part of a chord)

*: this is for two sines of the same (or close) amplitude. change the amplitudes: different effect

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Quote:
Original post by l0calh05t
if you add two sine waves with the frequencies f1 and f2 you will actually get a wave with the frequency f3 = (f1 + f2)/2 *but* this wave is amplitude modulated by another sine (actually cosine, but that's only a 90° phase difference and irrellevant in this case) wave with a frequency f3b = (f1 - f2)/2 thus if f1 and f2 are close together (ie f3b is low) it will sound like a single tone of the frequency f3 = (f1 + f2) / 2 with a fluctuating volume (beating)*, but if the difference between f1 and f2 (and thus f3b) is large it will sound more like something different, highly dependant on the frequencies chosen. for example if f2 is an integer multiple of f1 it will be part of the natural overtone series of f1 and thus most likely not audible as a separate pitch but as a change in tone/character. but if for example f2 = 2^(1/3) (3rd root of 2) it will sound more like a separate note. (in this case the third, thus forming part of a chord)

*: this is for two sines of the same (or close) amplitude. change the amplitudes: different effect


BRAINSSSSS!!!

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@samsonite

Brains indeed, cuz I wouldn't know it!

@the C modest god
The are uncountable amounts of notes

@Sean R Beeson
I know you! You're a heck of a good composer! Don't know where from I know you though

- Stenny

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@Samsonite: well, technically it's just high-school math... ;-)

edit: woo, 100th post, for an impressive posting rate of 0.05 posts/day

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