# Conversion

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

1. ### PGuest

How to convert decibel/decade to decibel/octave ?

2. ### ChrisGuest

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

http://en.wikipedia.org/wiki/Decibel

Just get out your calculator and do the math.

Cheers
Chris

3. ### PeteSGuest

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.

Cheers

PeteS

4. ### PGuest

Hi Pete,

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

Thanks,
P

5. ### PGuest

HI,

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

Thanks,
Prashanth

6. ### Don BoweyGuest

That's a really funny punch-line.
(snip)

Use google to search answers for your trollish questions.

Don

7. ### PeteSGuest

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
themselves.

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.

Cheers

PeteS

8. ### PuckdropperGuest

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.

Puckdropper

9. ### Bob EldGuest

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
Bob

10. ### jasenGuest

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

Bye.
Jasen

11. ### ChrisGuest

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.

Cheers
Chris

12. ### Bob MyersGuest

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 GarthGuest

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

14. ### jasenGuest

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).

Bye.
Jasen

15. ### Bob MastaGuest

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
dqatechATdaqartaDOTcom

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Home of DaqGen, the FREEWARE signal generator

16. ### Bob MyersGuest

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. ### kellGuest

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

18. ### Bob MastaGuest

I rest my case!

Bob Masta
dqatechATdaqartaDOTcom

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Home of DaqGen, the FREEWARE signal generator

19. ### Alan BGuest

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 BGuest

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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