base 10 so important in electronics ?why so

MrSoftware

Joined Oct 29, 2013
2,188
I just realized, I think the original poster may have been asking more about log base 10, as opposed to numbering system base-10. Two very different meanings of the same word "base". Maybe I'm late to the party in figuring out that this is really what he was asking. ;)

So the question re-worded (I think); why is log base 10 the common log, as opposed to some other log base. Does log base 10 happen to represent things in nature?

I think these two articles speak about why log base-10 is used often, and I found it really interesting:

https://en.wikipedia.org/wiki/Common_logarithm

https://en.wikipedia.org/wiki/Logarithm

Equally fascinating is the "natural log":

https://en.wikipedia.org/wiki/Natural_logarithm
 

wayneh

Joined Sep 9, 2010
17,496
If that's the case, I would say there is a very good reason why we call it the "natural log". I have no use for base 10 logs and consider them just an artifact of our favored numbering system.
 

ErnieM

Joined Apr 24, 2011
8,377
I always found it curious that an "octave" has no relationship to the number eight but instead denotes a doubling in frequency.

Plus, if you look at any keyboard there are twelve notes in each octave interval.
 

WBahn

Joined Mar 31, 2012
29,979
A, B, C, D, E, F, G, back to A.
Looks like 8 steps to me.
???

Step 1: A to B
Step 2: B to C
Step 3: C to D
Step 4: D to E
Step 5: E to F
Step 6: F to G
Step 7: G to A

Step 8: ????

However, like the fencepost problem, seven steps requires eight notes (and note that the two As are not the same note).

What I've sometimes pondered is why these notes are not equally spaced (logarithmically). Most are two semitones apart but B/C and E/F are only one semitone apart.

I've never found a solid justification for this and have concluded that it probably stems from what was considered "pleasing" to the human ear in whatever civilization originally crafted musical scales (which occurred before anyone had any notion of the frequencies associated with any of them). Certainly the choice of an octave (regardless of name) being a doubling in frequency was due to the recognition that two tones separated by an octave seemed equivalent in many regards and, hence, were given the same designation in the musical scale.

EDIT: Changed A/B to B/C to fix error pointed out by wayneh.
 
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wayneh

Joined Sep 9, 2010
17,496
Most are two semitones apart but A/B and E/F are only one semitone apart.
That's B/C, not A/B.

I recall reading an explanation of how music ended up the way it did - and it sort of made sense - but I seem to have forgotten most of it. The twelfth root of two and all that.

Per Wiki: "The most important musical scales are typically written using eight notes, and the interval between the first and last notes is an octave. For example, the C Major scale is typically written C D E F G A B C, the initial and final Cs being an octave apart. Two notes separated by an octave have the same letter name and are of the same pitch class."
 
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ErnieM

Joined Apr 24, 2011
8,377
A, B, C, D, E, F, G, back to A.
Looks like 8 steps to me.
Where did those arbitrary letters come from?

I said "look at a keyboard." They look like this:



Start just after the first key marked C (it's one of the short black ones) and count ALL the keys till you find the next C.

There are 12.

(As an aside, each of these adjacent keys differ in frequency by 2^1/12)
 
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WBahn

Joined Mar 31, 2012
29,979
Yes, there are 12 "semitones" in an octave. But the name comes from the number of raw notes (i.e., without accidentals) in an octave (including the notes at both ends -- so it counts the number of fence posts and not the number of fence sections).
 

AnalogKid

Joined Aug 1, 2013
10,987
Why base 10 is so important ,so famous,so applied ,so extensive use in logarithm? is this in nature?
base 10 is our own mathematical choice to understand nature or it is nature own choice to creation?
The natural logarithm, base e, is "in nature". Logarithmic, geometric, and other non-linear relationships are everywhere around us.

Base 10 is our choice because we have 10 fingers.

ak
 

Thread Starter

CIR.VINIT

Joined Feb 26, 2016
11
I just realized, I think the original poster may have been asking more about log base 10, as opposed to numbering system base-10. Two very different meanings of the same word "base". Maybe I'm late to the party in figuring out that this is really what he was asking. ;)

So the question re-worded (I think); why is log base 10 the common log, as opposed to some other log base. Does log base 10 happen to represent things in nature?

I think these two articles speak about why log base-10 is used often, and I found it really interesting:

https://en.wikipedia.org/wiki/Common_logarithm



https://en.wikipedia.org/wiki/Logarithm

Equally fascinating is the "natural log":

https://en.wikipedia.org/wiki/Natural_logarithm


Yeah!!! they are really interesting
 

WBahn

Joined Mar 31, 2012
29,979
BR-549, Actually one only needs on finger for binary. 1 or 0. :)
This is actually a relevant and subtle point.

For a positional base-10 system we need ten digits that represent the values 0 through 9.

But when we use our fingers to count things, we actually use eleven digits that represent 0 through 10 (zero being when no fingers are up). So while I do believe that we use a base-10 positional numbering system because we have ten digits on our hands (eight fingers and two thumbs), it is interesting that we seldom USE our ten digits the same way that we use digits in our number system.
 

GopherT

Joined Nov 23, 2012
8,009
Yes, there are 12 "semitones" in an octave. But the name comes from the number of raw notes (i.e., without accidentals) in an octave (including the notes at both ends -- so it counts the number of fence posts and not the number of fence sections).

While the human ear hears 7 notes per "octave", ABCDEFG, the sharps and minors are actually fill the gaps and make 12 EVENLY SPACED steps in each octave. The list below is the frequencies of the notes and then the right column is calculated from 220 with each additional step down the list by multiplying by 2^(1/12)

upload_2016-3-3_21-36-42.png
 

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WBahn

Joined Mar 31, 2012
29,979
While the human ear hears 7 notes per "octave", ABCDEFG, the sharps and minors are actually fill the gaps and make 12 EVENLY SPACED steps in each octave. The list below is the frequencies of the notes and then the right column is calculated from 220 with each additional step down the list by multiplying by 2^(1/12)
What does any of that have to do with why and octave is called an octave?

I have no idea what you mean when you say that the human ear hears seven notes per octave. The human ear is fully capable of not only hearing all twelve semitones, but is capable of distinguishing lots of other (unnamed) notes in between. For instance, people with "normal" hearing can distinguish frequency differences of just 4 Hz at 2000 Hz, which is between B6 and C7 but those two semitones are separated by nearly 120 Hz.
 

GopherT

Joined Nov 23, 2012
8,009
What does any of that have to do with why and octave is called an octave?

I have no idea what you mean when you say that the human ear hears seven notes per octave. The human ear is fully capable of not only hearing all twelve semitones, but is capable of distinguishing lots of other (unnamed) notes in between. For instance, people with "normal" hearing can distinguish frequency differences of just 4 Hz at 2000 Hz, which is between B6 and C7 but those two semitones are separated by nearly 120 Hz.
The human ear hears what seems to be seven logical progressions and 5 that seem "off" and, therefor called minors or sharps.
 

WBahn

Joined Mar 31, 2012
29,979
The human ear hears what seems to be seven logical progressions and 5 that seem "off" and, therefor called minors or sharps.
There's nothing special about the C-major scale (the only one that doesn't use accidentals). That "we" find it (and the other major scales) somehow "natural" is merely a product of culture because it is the scale that we are most used to hearing. It itself is an evolution of other scalings and other cultures have different scalings that can't even be played on most western instruments (a slide trombone being one exception since it can be continuously tuned) and they find our major scales unnatural -- or "exotic" at best-- just as we do theirs.
 

GopherT

Joined Nov 23, 2012
8,009
There's nothing special about the C-major scale (the only one that doesn't use accidentals). That "we" find it (and the other major scales) somehow "natural" is merely a product of culture because it is the scale that we are most used to hearing. It itself is an evolution of other scalings and other cultures have different scalings that can't even be played on most western instruments (a slide trombone being one exception since it can be continuously tuned) and they find our major scales unnatural -- or "exotic" at best-- just as we do theirs.
Exactly. Good work.
 
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