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Twelfth root of two

Technically, this has nothing to do with Deep Purple. Or everything to do, depending on how you look at it. There was a discussion some tome ago in our comments about the connection between music and math, and then this video came across our attention. In half an hour it explains the fundamental mathematical problem with music, and how a solution (kinda sorta) to it was adopted in European music circa the times of J.S. Bach.

15 Comments to “Twelfth root of two”:

  1. 1
    Uwe Hornung says:

    I don’t get all the math, but I prefer the sound of the equal temperament at 28:20 to the just intonation at 28:49, both in original tuning. I find the “slight roughness” of the first version more expressive and vibrant, the just intonation sounds kind of dead to me. I had the same experience when I played (‘playing’ is an overstatement, I hit a few chords, I can’t play piano) years back on an electric piano at the Frankfurt music fair where you could switch between equal temperament and just intonation – the latter didn’t do anything for me. But then of course we have all been exposed to music played by instruments in equal temperament for all our lives – we’re creatures of habit.

    It’s not just an issue on piano either, a guitar tuned perfectly to sound great when playing one chord can sound out of tune when playing another chord.


    And dual guitar lines à la Wishbone Ash or Thin Lizzy will sometimes sound better if the tuning of the two guitars does not match 100%.

  2. 2
    Gregster says:


    That was really, really good imo, though the narration was a little mehh, & sounded more like A.I. monotone than a real person lol ! Thanks for posting !

    Important for people to remember here that the intonation issue lay with keyboard instruments only…Every other musical instrument can be subtly adjusted in real-time by the musician into agreeable tune.

    * And it doesn’t matter whether you’re tuning to 440-Hz, or the much more agreeable & universally-friendly 432-Hz, the issue is with the ratios between intervals, not the cycles-per-second value.

    I’ve linked here a very good film, that everyone will benefit from, & is arguably much easier to digest. Leonard Bernstein was great at teaching, & all musicians will benefit greatly from its viewing. ( The full version is over 2-hours-long, attached is the short important bit lol )


    Peace !

  3. 3
    Uwe Hornung says:

    A Yank pushing for a lower rather than a higher concert pitch?! What’s the world coming to! ; – )

    I pledge allegiance to the internationally recognized concert pitch of 440 Hz !

  4. 4
    Gregster says:

    @3 LOL ! Apparently, scientists have in recent times ( once again ) placed a board & sand onto a speaker laid horizontally on the ground, & photographed the imagery created by the sands movement on the board, when music was played that was tuned into both pitches. The geometric art-work displayed at 432-Hz needs to be seen to be believed ! 432-Hz resonates with our universes preferred / natural standard pitch / vibration. Check-out the images linked.

    Also, the “rumor-mil”l once said that 1/2 of the success of “Dark Side of the Moon” was because the band tuned to 432-Hz, & this caught everyone’s attention, due to its natural , agreeable appeal. ( Or perhaps they slowed the tape-speed down ever-so-slightly ).

    That said, as long as everyone is in tune using a tuner @ 440-Hz, the music will still sound good.


    Peace !

  5. 5
    Kevin says:

    I have read where Ritchie gave some credit to his father for helping him with his music-guitar lessons because he was a mathematician or good at math back when he was a teen. So RB evidently was taught about the mathematical correlations with music way back then.

  6. 6
    Nick Soveiko says:

    Gregster @4:
    more likely, 432Hz is the resonant frequency of the vessel this picture was taken, and not the whole universe 😉

  7. 7
    Uwe Hornung says:

    (assumes lotus position – if you’re 62 like me that means: ouch! -, folds hands & takes deep breath)

    OMMM … (or: AUMMM …)


    THE SHIVA STAR – where, uhum, smashed TV cameras, esoteric tranquility and your own personal karma indissolubly merge …


    I kinda like the thought of spiritual/universal frequency though, hadn’t heard of it up to now – you’ve converted me!

  8. 8
    Gregster says:

    @6 Yes indeed ! Difficult to capture a picture of the whole universe lol !

    That said, there are a lot of images available of all-sorts taken of “things” resonating at the 432-Hz range. Simply google 432-Hz images & go for it.

    The frequency has been known about for a long,long time. I remember playing in my high-school brass-band & people were discussing it in the 1980’s. So it’s a well-known frequency, that’s for sure. I wouldn’t be surprised to learn that it was known about centuries ago. This article indicates 1874 for its consideration of being the standard pitch to be used.


    Peace !

  9. 9
    Reinder Dijkhuis says:

    Reuters fact-checked a number of claims about 432 Hz so I don’t have to:

  10. 10
    Nick Soveiko says:

    Reinder @9:


  11. 11
    Uwe Hornung says:

    Sad, another urban myth shattered. ; – ) You just did to it, Reinder, what those Lancaster Dambusters did to our Edertalsperre!


    And we’ve learned that not even the Nazis can be blamed for everything.

  12. 12
    Gregster says:

    @ 9 & 10…

    Well, a picture says 1,000 words imo.

    Peace !

  13. 13
    MacGregor says:

    Good old Pythagoras eh? I try to keep an open mind to many things in this world & I have read a little about the Harmonic Balance theory over the years. We all know how rhythm affects us animals (humans) & also musical notes, whether created by ourselves or nature. Also the Chakras of our body according to those Eastern beliefs & the relationship to different intonation etc. It doesn’t hurt to use the mind & think a little, as John Lennon once said, ‘I go somewhere all the time, it’s called my mind’. We think what we think & some of it is good & some of it just theories etc. Thanks for the link & also to Gregster for the Bernstein clip, interesting indeed. I also remember reading many years ago those tests that were completed on music & it’s effects on plants. Classical music played loud & repeatedly (obviously mild & serene music, not Wagner etc) & hard rock heavy metal etc. The indoor plant next to the classical music speaker didn’t move at all over the specified time period.. The replica plant of the same age, size, seed & health etc next to the hard rock & metal speaker was gradually leaning away from that speaker. All scientifically completed under strict controlled conditions apparently. Obviously sound waves create a vibration as we know. Some are harsher & more abrasive than others. It always comes back to those pesky rockers & their long hair & noisy habits. A pest on planet Earth indeed it seems. I also remember the Buddhist saying “Believe nothing”. It is all good either way. Cheers.

  14. 14
    Gregster says:

    @13…Good post Sir ! And darn those plants… It’s not our issue if they can’t learn to (qt GH ) “- Be shakin’ their asses to the left, & shakin’ their asses to the right”…LOL !

    I have the full Bernstein film, & it’s well worth watching the whole thing if anyone has the time ( downloaded from You-Tube ). Possibly the best aspect is how the revealing of the Gb/F# pentatonic scale naturally appears after following the cycle-of-5th’s. ( These are all the black keys/notes on the piano starting from Gb/F# ), & how important it is to us in our music. What wasn’t mentioned graphically was the Cycle of 4th’s & 5th’s, & other important aspects of this “wheel”…But it was only an overview lol !

    Interesting to note that the full version of the lecture has Mr.Bernstein apologizing to the people who attended, since the lecture had to be spread-out over 2-days, due to a bomb-threat-scare…Hmmm…

    Peace !

  15. 15
    Dr. Bob says:

    That was more interesting than I expected. I understand the math better than the music.

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