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Discussion in 'Electronic Basics' started by P, Aug 31, 2006.

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  1. P

    P Guest

    How to convert decibel/decade to decibel/octave ?
  2. Chris

    Chris Guest

    20dB/decade = approx. 6dB/octave
    10dB/decade = approx. 3dB/octave.

    Just get out your calculator and do the math.

  3. PeteS

    PeteS Guest

    To convert from any base x to any other base y, take ln(y) / ln(x). In
    this case, the conversion factor is 3.322 (to three decimal places). In
    fact, you can take log[arbitrary base]y / log [same arbitrary base] x
    and get the same result.


  4. P

    P Guest

    Hi Pete,

    Thanks for replying. I dint quite understand how you 3.322. Would be
    greta if you could add some more explanation.

  5. P

    P Guest


    Also could somebody tell me what decade and octave stand for ?


  6. Don Bowey

    Don Bowey Guest

    That's a really funny punch-line.

    Use google to search answers for your trollish questions.

  7. PeteS

    PeteS Guest

    First, bottom post. It's netiquette in these parts for the very good
    reasons that top posting (which you did) makes it impossible to read
    the thread as it expands.
    Not doing the right thing [tm] gives those of us who happen to use
    google mail and google groups for convenience a bad name.

    Second, as you don't know what a decade or an octave is, I am not
    surprised you don't understand the answer I gave.

    So you are either trying to do homework on a very incomplete course, or
    you are trying to find out how to confirn some answers from a random
    book. I would suggest, as others have, that you look for the
    definitions of decade and octave. We tend to help those who help

    There is a number associated with decade and likewise octave. If you
    plug those into the equation you will find the anwer above.

    Incidentally, you can empirically confirm the answer if you know basic
    filter theory (rolloff is at a rate (simplistically and for a single
    pole filter) of 6dB/octave and 20dB/decade and they are related by the
    value I gave above.


  8. Puckdropper

    Puckdropper Guest

    Now you got me curious. I did a quick wikipedia lookup, and found out
    what a decade in this context means. It took a whole 5 minutes to do.

    My note to everyone: please take the time to do a quick search before
    posting questions... It only takes a minute, and you get a faster reward.

  9. Bob Eld

    Bob Eld Guest

    A decade is a ratio of 10 to1. dB = 20log(ratio). So, a decade in dB is 20
    times the log of 10 = 20 times 1 = 20 dB.

    An octave is 2 to 1, so an octave in dB = 20 times the log of 2 = 20 times
    0.30103 = 6.02 dB. An octave which means eight is 2 to 1 not 8 to 1 as one
    might think. It's 2 to 1 because of its association with sound and music not
    because it makes any sense to use that word, confused?

    To convert from one to the other, add or subtract 14 dB. Check: 10 to 1
    divided by 2 to 1 = 5 to 1. dB for 5 to 1 = 20 times the log of 5 = 20 times
    0.699 = 13.98 dB. Likewise 20 - 6.02 = 13.98
  10. jasen

    jasen Guest

    decade - ten of something - in this case a multiplication factor of 10

    octave "8" major notes: C D E F G A B C (that's 7 by my count)
    for a doubling in frequency or a multiplication factor of 2

  11. Chris

    Chris Guest

    Let's take 10dB per decade. Divide 10 by 3.322 and you get about 3.01,
    so it would be 3.01dB per octave.

    If it's 20dB per decade, it's also 6.02dB per octave.

    Everyone just rounds it off to 6 and 3.

  12. Bob Myers

    Bob Myers Guest

    Seven different labels for the notes, but in music an "octave"
    is considered as including both the fundamental (first note
    in the scale) and its second harmonic (the last in the scale,
    which has the same "name" as the fundamental). A chromatic
    scale actually has 12 notes, not 8, as it includes the additional
    tones which are "valid" for use in that key.

    Bob M.
  13. Lord Garth

    Lord Garth Guest

    Right! Don't forget the sharps and flats Jasen. If I recall correctly,
    the are half way between notes.
  14. jasen

    jasen Guest

    I still see seven steps..

    if you're including both end-points there are 13 , but yeah 12 steps.
    Half way between some of them (on an even tempered (musical) and log
    (frequency) scale).

  15. Bob Masta

    Bob Masta Guest

    All conventional Western music uses the "equal tempered" scale,
    in which each semitone is 2^(1/12) from its neighbor... about 6%.
    If you apply this 12 times, you get 2^(12/12) = 2 = 1 octave.
    An octave on a keyboard instrument (piano, organ, etc) has 12
    (white and black) keys. The above 12th root applies between *any*
    adjacent keys, white or black. So there is the same step between
    B and C (which have no intervening black key) as between C and C#.

    The "whole" and "half" step (or note) adjectives that musicians use
    seem needlessly confusing. To my mind, conventional music theory
    and notation must have grown by accretion or something... it hardly
    looks like a rational system.

    Just my 2 cents worth... ;-)

    Bob Masta

    D A Q A R T A
    Data AcQuisition And Real-Time Analysis
    Home of DaqGen, the FREEWARE signal generator
  16. Bob Myers

    Bob Myers Guest

    Seven steps, but eight notes. If you count from
    1 to 8, there are only seven "steps" between the "1"
    and the "8," right? What's so hard about this?

    Bob M.
  17. kell

    kell Guest

    The Circle of Fifths.
    Start with a tonic and go up by intervals of a fifth (C -> G -> D -> A
    You will get the seven notes of the traditional diatonic scale.
    After that, you start getting into the "accidentals," the sharps and
  18. Bob Masta

    Bob Masta Guest

    I rest my case!

    Bob Masta

    D A Q A R T A
    Data AcQuisition And Real-Time Analysis
    Home of DaqGen, the FREEWARE signal generator
  19. Alan B

    Alan B Guest

    Well, it's confusing to me also, but I'm not sure it's needlessly so. The
    positioning of the half-steps separate major scales from minor, and the
    inclusion or exclusion of flats and sharps define the key. The differences
    are completely subjective with regards to the interpretation of the human
    ear, yet nevertheless very real. It's all Bach's fault.
  20. Alan B

    Alan B Guest

    But if you tapped out the octave on a piano, you'd hear eight.

    A-B-C-D-E-F-G-A' (A-prime) if that makes more sense?
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