Ælberiigor
Active member
- Joined
- Dec 1, 2023
- Messages
- 781
You are fully right !
Admit a C vibrating at 1Hz. 1Hz is 1 pulse per second, and the second like the meter should be related to the proportions of the Earth.
The next octave is two tome higher and so on : 1Hz, 2Hz, 4Hz, 8, 16, 32, 64, 128, 256, 512Hz... are all C (C0, C1. C2...C9).
What is the frequency of A ? to upgrade to the next octave you multiply by 2, to shift from one semitone to another you have to multiply
There is even an article (I didn't read but stole the 12th_root_of_2 image) about : https://en.wikipedia.org/wiki/Twelfth_root_of_two
= 1.059463094
To shift up more, you elevate the power (exponent) and multiply by this value, for 3 the factor is (
) ^3
Semitones are : C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C
From C to the next A, you have to shift 9 times, so you multiply the C frequency by (
) ^9, up to discover than 432 is not in list of value :
The table cover from C8 (=256Hz) to C9 (=512Hz), and the 12th root of 2 is noted f
The fourth column is the degree name
There is no 432Hz in the table, the correspondent A is 430.539.
But in this case, I follow the neutral tuning. I means that C sharp is the same as D flat (like on a piano)
During the Baruch period musicians used a Tempered Tuning. Listen Harpsichord sonatas (Rameau...) if you don't know.
I can't provide concise details about, and several tempered tuning has been developed.
What I know is that tones can be divided in 9 comas, making :
- C to D being 1 tone, so D is 9 comas higher than C
- C sharp being C shift up by 4 comas
- D flat being D shift down by 4 comas
So C sharp is not the same frequency than D flat, and maybe you found your A 432Hz in this model.
Note that violinist are required to learn it, making violin the most complicate instrument with the piano for a totally different reason.
How to compute the frequency of A in this model ? Is there really a A 432Hz in a tempered model ?
But for sure, A 440Hz is not in phase with our world
I also love music and have a look on the 432Hz in the past, and it's very interesting :Don't fall for the 432 propaganda either. I have found much better frequencies. 451, 466, and 486 are expressive, bright, and full tone which allows science and art to flow togther beautifully. 440 is dull, dead, and restrictive.
Admit a C vibrating at 1Hz. 1Hz is 1 pulse per second, and the second like the meter should be related to the proportions of the Earth.
The next octave is two tome higher and so on : 1Hz, 2Hz, 4Hz, 8, 16, 32, 64, 128, 256, 512Hz... are all C (C0, C1. C2...C9).
What is the frequency of A ? to upgrade to the next octave you multiply by 2, to shift from one semitone to another you have to multiply
There is even an article (I didn't read but stole the 12th_root_of_2 image) about : https://en.wikipedia.org/wiki/Twelfth_root_of_two
To shift up more, you elevate the power (exponent) and multiply by this value, for 3 the factor is (
Semitones are : C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C
From C to the next A, you have to shift 9 times, so you multiply the C frequency by (
The table cover from C8 (=256Hz) to C9 (=512Hz), and the 12th root of 2 is noted f
Open a javascript console in your browser (Ctrl+shift+C) :
Math.pow(2, 1/12) // is the 12th root of 2 javascript notation
256 * Math.pow(Math.pow(2, 1/12), N) // compute a frequency, N being the semitone shift from 0 (tonic) to 12 (octave)
Math.pow(2, 1/12) // is the 12th root of 2 javascript notation
256 * Math.pow(Math.pow(2, 1/12), N) // compute a frequency, N being the semitone shift from 0 (tonic) to 12 (octave)
| C | 256 * f⁰ | 256 | tonic |
| C# | 256 * f¹ | 271.223 | minor second |
| D | 256 * f² | 287.350 | major second |
| D# | 256 * f³ | 304.437 | minor third |
| E | 256 * f⁴ | 322.540 | major third |
| F | 256 * f⁵ | 341.719 | fourth |
| F# | 256 * f⁶ | 362.039 | augmented fourth or diminished fifth or tritone |
| G | 256 * f⁷ | 383.567 | fifth |
| G# | 256 * f⁸ | 406.375 | minor sixth |
| A | 256 * f⁹ | 430.539 | major sixth |
| A# | 256 * f¹⁰ | 456.140 | minor seventh |
| B | 256 * f¹¹ | 483.264 | major seventh |
| C | 256 * f¹² | 512 | octave |
But in this case, I follow the neutral tuning. I means that C sharp is the same as D flat (like on a piano)
During the Baruch period musicians used a Tempered Tuning. Listen Harpsichord sonatas (Rameau...) if you don't know.
I can't provide concise details about, and several tempered tuning has been developed.
What I know is that tones can be divided in 9 comas, making :
- C to D being 1 tone, so D is 9 comas higher than C
- C sharp being C shift up by 4 comas
- D flat being D shift down by 4 comas
So C sharp is not the same frequency than D flat, and maybe you found your A 432Hz in this model.
Note that violinist are required to learn it, making violin the most complicate instrument with the piano for a totally different reason.
How to compute the frequency of A in this model ? Is there really a A 432Hz in a tempered model ?
But for sure, A 440Hz is not in phase with our world

