A = 432 Hz vs. A = 440 Hz


In this video I tuned my guitar to concert pitch A=432 Hz.  Which is slightly lower than the standard concert pitch A=440 Hz.

Although I tuned to A=432 Hz, instead of the standard A=440 Hz, this is still not a genuine Pythagorean tuning.  This is because instruments are tuned using the Equal Temperament Scale.

According to the Pythagorean tuning, or “Just Tuning” scale A=432 Hz, and C=128 Hz… (there are more)  And they function according to fibonacci sequence, and therefore is the most harmonious tuning to our being.
(Since this spiral is used in our inner ears).

The only issue with REAL Just Tuning is what’s known as a “Wolf Interval,” so an A# and a B flat, which are normally the same note, are actually slightly off.

So if you wanted to play in a different key you would have to re-tune your piano or guitar for EACH SONG.  Yikes!!!!

The “Equal Temperament Scale” was designed to have the least amount of these so called “bad” intervals, so it’s not as perfectly harmonious as “Just” Tuning, BUT you don’t have to re-tune your instrument for each song!
(which would make live concerts really annoying!)

According to our A=440 Hz Equal Tempered tuning, our C is 130.18 Hz,

So by subtracting 8 Hz from 440, we get 432, and then by default we automatically subtract 8 Hz from C=130.18, we get a C=122.81 Hz !!!!!!!

(And not the C=128 Hz like in Pythagorean Tuning)

So by making the A more resonate, we in turn make the C further away.

According to Pythagorean / “Just” Tuning:

C = 128 Hz
G =192 Hz
D = 288 Hz
E = 324 Hz
A = 432 Hz

And our current A= 440 Hz / Equal Temperament Tuning is:

C = 130.81
G = 196.00
D = 293.66
E = 329.63
A = 440.00

SO when subtract 8 Hz from all of these, and you’ll get what my guitar is tuned to in this video, which IS NOT true Pythagorean tuning!!!  Some note’s are slightly closer to the Pythagorean notes (usually by 4 Hz), but the C is still further away.

So why did I tune to this?  Many site’s suggest that we should change our concert pitch to A=432 Hz (C= 128 Hz).  I originally assumed that by doing this my chords would become more harmonious, but as I have shown, this is fundamentally impossible!

Overall, using this tuning makes it significantly easier to sing certain songs, even if the pitch is only a tad lower.  I wouldn’t have covered this song without the tuning cause it’s hard as heck to sing normally!

 

Online Sources:

Frequencies of Musical Notes:
http://www.phy.mtu.edu/~suits/notefreqs.html

Pythagorean Tuning:
http://www.sccs.swarthmore.edu/users/08/ajb/tmve/wiki100k/docs/Pythagorean_tuning.html

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3 thoughts on “A = 432 Hz vs. A = 440 Hz

  1. krustybeats says:

    Hi,

    Nice article! Very useful information here.

    I have been looking for ways to get the real Pythagorean tuning. Initially I was under the impression that just by tuning down 8 Hz to get A=432Hz would give me the Pythagorean tuning. Then i figured that that wouldn’t be enough, since it’s the relationship between the frequencies of notes within a scale that matters.

    Now, that i’ve tested this out myself with a tuning plugin, i see that just tuning down -32cents within a DAW would indeed give me the real Pythagorean tuning. Is this possible? I’m using FL Studio and it has the master tuning option available. Are you using some kind of a DAW and can you comment on that? After tuning down -32cents, the native plugins in FL show the correct frequencies of Pythagorean tuning when played, i.e.:

    C = 128 Hz
    G =192 Hz
    D = 288 Hz
    E = 324 Hz
    A = 432 Hz

    I’d appreciate if you could answer.
    Peace

  2. Sue Terry says:

    Hi John,
    Just wanted to mention a couple of things–first, I love your cover of Winter Hymnal and I think it’s actually much better than the original. The other thing is–keep in mind you can’t just subtract 8 hz from every frequency to get the rest of the pitches, it doesn’t work that way. That said, I hope you’ll keep experimenting because that’s how we learn and that’s how music can evolve. I agree with you that the A=432 tuning is better than A 440. There seems to be a lot of fan interest in the idea, but I don’t see many musicians using the 432 tuning, unfortunately. Perhaps this will change. Feel free to contact me if you like, anytime. All best to you–
    Music power,
    ‘Sweet’ Sue Terry

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