Zarlino

Various internet trolls will argue, quite violently, that A=432 Hz is a dirty, stinking lie – and that there is no historical record of it ever being… bla, bla, bla.

 While we agree that A is not the foundation of resonance (B-flat is), the “A” note, nevertheless, at 432 Hz nonetheless is a harmonic of our B-flat reference pitch – and there is at least one documentation of this which survives to this day.

Gioseffo Zarlino (31 January or 22 March 1517 – 4 February 1590) was the leading music theorist of his day, based in Venice – which was the most powerful European city-state at the time.
One day, at an exhibition of Venetian art in Portland, Oregon – they just happened to be displaying Zarlino’s book Le Istitutioni Harmoniche, opened to page 104:
Zarlino frequencies
 … which handily lists a bunch of frequencies.
If we take a look at those frequencies and compare them to the frequencies we generated as harmonics from our magic frequencies of 5.4 Hz and 7.2 Hz, we get the results listed in the table, below.
Zarlino table.png
  • In the second column, the frequencies in the first column have been divided by 2 a few times to bring them into familiar octaves
  • The third column adds up the digits of each frequency, numerologically and reveals that most of them factor to 9
  • The fourth column indicates (in red) if these frequencies exactly match the harmonic frequency for that note as we determined it, from our “magic” base frequencies of 5.4 Hz and 7.2 Hz – and indicates in black if they are close matches
  • The last column highlights in red where Zarlino’s frequencies match our frequency for that note when a different sequence of harmonics is used than the one we chose
    • Being as Zarlino was an intelligent fellow, we’ll keep track of his frequencies in case they are useful when it comes to the practicalities of building a Just Intonation musical instrument

To summarize the findings – of the eight notes that Zarlino lists, A, B, C, C#, D, E, F#, G:

  • Four of them match our harmonic frequencies, exactly – A, B, D, E
  • Three more match our harmonic frequencies exactly if we use a different sequence of harmonics to derive them – still based on our B-flat starting frequency of 7.2 Hz:  C#, F#, G
  • The only one that’s a miss is C  – probably because he perhaps wanted to take the simplistic approach that 1 x 2 = 2, 2 x 2 = 4, 4 x 2 = 8, 8 x 2 = 16, 16 x 2 = 32,
    32 x 2 = 64, 64 x 2 = 128, and 128 x 2 = 256.  In other words, for this one note, he seems to have determined this note mathematically – (and perhaps this is the correct frequency.  We’ll keep that one in our hat, also)

I’m not going to argue with Zarlino on the correct way to determine the harmonic frequencies – what is significant here is that we came up with a bunch of musical frequencies based on a chance encounter with vibration in a Johannesburg hotel room – and those frequencies, one way or another, also match what Zarlino recorded in his book published in 1558.

How is this possible?  Well, first of all, Zarlino was the first advocate in Western culture for Just Intonation.  Secondly, he must have started with the same frequencies as I did in order to calculate his just, harmonic series; either that, or the frequencies were passed down to him from some earlier culture.  I will have to read his book to find out.

Just another confirmation from history that we are on the right track with these frequencies.