Some on the internet maintain, often vehemently, that A=432 Hz is a dirty stinking lie – and that there is no historical record of it ever being… bla, bla, bla.
However, there is at least one piece of documentation which survives to this day – which I was lucky enough to bump into, around 2012.
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 have Zarlino’s book Le Istitutioni Harmoniche, opened to page 104 – which shows a lot of interesting numbers, as well as “ut-re-mi-fa-sol-la“. We don’t know what happened to “ti” and “do” – but the numbers themselves warranted taking a picture, which you see here:
Above, I have taken those numbers and octaved them down so they are recognisable – and you can see an overlap with the Earth harmonic-series: the “third column” of frequencies. Precisely – except for C# and F# which are close.
Zarlino’s Harmonic Intervals:
In his books, Zarlino developed Pythagoras’ view of harmonic fractions, to come up with the following intervals. It does seem that he used A = 432 Hz as his “generator” frequency for the the rest of his just-intonation scale – applying the ratios of 3:2 (third harmonic), 9:8 (ninth harmonic), 3:4 (third harmonic below) to generate the different frequencies as harmonics of each other:
| Starting Frequency | Harmonic Treatment | Resulting Frequency |
|---|---|---|
| C as 256 Hz | x 3 x 2 (3rd harmonic) | = 384 Hz: G |
| G as 384 Hz | x 3 x 2 (3rd harmonic) | = 288 Hz: D |
| D as 288 Hz | x 3 x 2 (3rd harmonic) | = 432 Hz: A |
| A as 432 Hz | x 3 x 2 (3rd harmonic) | = 324 Hz: E |
| E as 324 Hz | x 3 x 2 (3rd harmonic) | = 486 Hz: B |
| B as 486 Hz | x 3 x 2 (3rd harmonic) | = 364.5 Hz: F# |
| F# as 364.5 Hz | x 3 x 2 (3rd harmonic) | = 273.375 Hz: C# |
In sequence, this 8-note collection of Zarlino harmonic notes is: A B C C# D E F# G
Zarlino was the first advocate in Western culture, that I know about (unless you count Pythagoras) for Just-Intonation (i.e. harmonic tuning) – in this case, based on A 432 Hz. A scale derived harmonically using whole-number multipliers.
Where he got the idea that C should be 256 Hz, I don’t know. Rudolf Steiner also believed C should be 256 Hz. Either way, it’s part of the Earth’s harmonic series – as is A 432 Hz – as the 5th harmonic (major third interval, “do re mi” of the F 10.8 Hz frequency I detected on a frequency generator.
Is it just a coincidence that Zarlino developed a tuning in-tune with Nature’s resonance? Or did he have some ancient knowledge, or experimental insight which allowed him to choose these starting frequencies?
Perhaps if we can read his books in Italian we’ll be able to find out.
So this is a piece of corroborating evidence from history that we are on the right track with these frequencies. And also, an interesting insight that 432 Hz has a known historical provenance in Western music history going back to at least the 16th Century.
Verdi
Verdi is often credited with using A 432 Hz – and for writing a letter to the Italian government referencing it, in 1884. But the internet has already declared that he was only wanting to lower the pitch somewhat for the sake of his opera singer, and that he wasn’t bothered to what.
So, Zarlino goes back 300 years before Verdi.
Zarlino in Action
Anyway, here’s a little of my light piano skills, playing a “harpsichord” sound tuned to Zarlino’s frequencies, and playing only his frequencies. It’s quite a nice-sounding tuning, enjoy!