Welcome to the Piano World Piano Forums
Over 2.5 million posts about pianos, digital pianos, and all types of keyboard instruments
Join the World's Largest Community of Piano Lovers (it's free)
It's Fun to Play the Piano ... Please Pass It On!

SEARCH
Piano Forums & Piano World
Find a Professional
Our Classified Ads
Find Piano Professionals-

*Piano Dealers - Piano Stores
*Piano Tuners
*Piano Teachers
*Piano Movers
*Piano Restorations
*Piano Manufacturers

Advertise on Piano World

What's Hot!!
Posting Pictures on the Forums
-------------------
Forums RULES & HELP
-------------------
ADVERTISE on Piano World
(125ad)
Piano Life Saver - Dampp Chaser
Dampp Chaser Piano Life Saver
(ad)
Piano Buyer Guide
Piano Buyer Fall 2017
Who's Online Now
126 registered members (anamnesis, adurx, Beakybird, AndyP, AZNpiano, anotherscott, 30 invisible), 1,442 guests, and 1 spider.
Key: Admin, Global Mod, Mod
(ad)
Estonia Pianos
Estonia Pianos
Quick Links to Useful Piano & Music Resources
Quick Links:
*Advertise On Piano World
*Free Piano Newsletter
*Online Piano Recitals
*Piano Recitals Index
*Piano & Music Accessories
*Live Piano Venues
*Music School Listings
* Buying a Piano
*Buying A Acoustic Piano
*Buying a Digital Piano
*Pianos for Sale
*Sell Your Piano
*How Old is My Piano?
*Directory/Site Map
*Virtual Piano
*Music Word Search
*Piano Videos
*Virtual Piano Chords & Scales
Previous Thread
Next Thread
Print Thread
#2122598 - 07/24/13 11:45 PM OT ... why base 10?  
Joined: Jul 2004
Posts: 6,150
Dave Horne Online content
6000 Post Club Member
Dave Horne  Online Content
6000 Post Club Member

Joined: Jul 2004
Posts: 6,150
Vught, The Netherlands
I had a discussion with my son-in-law about this.

Is our system of counting, base 10, anthropomorphically based (since we have ten fingers)? If beings elsewhere in the universe have eight fingers, would they use a base eight system of counting?

Is there anything special or easier about using a base ten system?




website | mp3 files | Yamaha AvantGrand N3 | Roland RD 2000 | Sennheiser HD 598 headphones
(ad) ROLAND

Click Here

#2122612 - 07/25/13 12:37 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: Feb 2010
Posts: 4,880
wouter79 Offline
4000 Post Club Member
wouter79  Offline
4000 Post Club Member

Joined: Feb 2010
Posts: 4,880
>If beings elsewhere in the universe have eight fingers, would they use a base eight system of counting?

No not necessarily. Other civilizations used 12-based (duodecimal), and we also seem to use it for the clock time? In computer science we all use 2-based.

A complete list is here

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


[Linked Image][Linked Image][Linked Image][Linked Image]
#2122696 - 07/25/13 07:02 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: May 2011
Posts: 1,247
maurus Offline
1000 Post Club Member
maurus  Offline
1000 Post Club Member

Joined: May 2011
Posts: 1,247
Interesting that you ask this question on a piano forum. Of course, for us the 10 fingers are crucial... wink

And yes, the main reason historically for a base 10 system seems to be the anatomical coincidence and the resulting practice of counting with fingers.

There were, and there are, alternative systems that have mathematical advantages. Some of them are also part of the modern baggage here ore there:

Systems with base 12 ('a dozen', 12 months, 2x12 hours a day, ...) have their advantages (they allow easy division by 2,3,4 and 6), and the Mesopotamian sexagesimal system with base 5x12=60 (even more easy divisors) was perhaps the best from a mathematical point of view. It is still at work in our measurement of time (an hour has 60 mins, a minute has 60 seconds) and of the circle (6x60 degrees, 1 degree = 60', 1'=60"...).

Some languages have remnants of a system with base 20 (see the French 'quatre-vingt' or Danish 'firsindstyve').

Otherwise, see the list linked above...

#2122697 - 07/25/13 07:10 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: Jul 2013
Posts: 46
Big McLargehuge Offline
Full Member
Big McLargehuge  Offline
Full Member

Joined: Jul 2013
Posts: 46
I see other systems in numerous science fiction novels and stories, I always find that kind of thing interesting, authors thinking of all the ways aliens (or changed humans) will be different from us.

(ad)
Piano & Music Accessories
piano accessories music gifts tuning and moving equipment
#2122703 - 07/25/13 07:42 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: Dec 2010
Posts: 2,206
rnaple Offline

Silver Supporter until April 24 2014
rnaple  Offline

Silver Supporter until April 24 2014


Joined: Dec 2010
Posts: 2,206
Rocky Mountains
I don't know why I mention this. Maybe I'm just stupid. From my very shallow knowledge of string theory. There are 11 strings. Less are incomplete. More are unstable. Here's where I probably fault....just off the top of my head... zero through ten make eleven. There is something special about eleven strings. Just something to think about.


Ron
Your brain is a sponge. Keep it wet. Mary Gae George
The focus of your personal practice is discipline. Not numbers. Scott Sonnon
[Linked Image][Linked Image]
#2122709 - 07/25/13 08:15 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: Jul 2011
Posts: 3,033
dire tonic Offline
3000 Post Club Member
dire tonic  Offline
3000 Post Club Member

Joined: Jul 2011
Posts: 3,033
uk south
Quote
Is there anything special or easier about using a base ten system?


No, nothing at all, apart from the ease of multiplying and dividing by 10 which is a doddle.

Any integer can be used as a numbering base. It would be hard to ascribe a uniqueness in quality to any integer other than a cultural significance arising through folklore or, as you point out, a match for the number of digits in our 2 hands. Integers do have collective qualites and can become members of sets according to simple arithmetical or algebraic rules and qualities; even, odd, prime, integer squares, almost anything you want to make up really. But none of those qualities give a number pre-eminence as a base for a numbering system.

Years ago when I was messing with simple programming I had to get used to hexadecimal (base 16) which is all well and good until you get to the number 10 (decimal) which requires its own symbol, in this case 'A'. So you have.

(dec - hex)
0 = 0
1 = 1
2 = 2
3 = 3
4 = 4
5 = 5
6 = 6
7 = 7
8 = 8
9 = 9
10 = A
11 = B
12 = C
13 = D
14 = E
15 = F
16 (decimal) = 10 (hex)

So hex(adecimal) is great for multiplying and dividing by (decimal)16 if that's what you want to do.

And there's the rub; for higher magnitude numbering bases, you need even more symbols.

#2122725 - 07/25/13 09:20 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: Sep 2011
Posts: 20
Peter Leyssens Offline
Full Member
Peter Leyssens  Offline
Full Member

Joined: Sep 2011
Posts: 20
Leuven, Belgium
As a matter of fact, you can still find remnants of 12 and 16 base counting in many languages. For example, in English, we count up to twelve before we switch to three-teen, four-teen, ... In French, it goes up to seize (sixteen) before it continues with dix-sept (ten-seven).

#2122743 - 07/25/13 09:55 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: Feb 2010
Posts: 4,339
anotherscott Online content
4000 Post Club Member
anotherscott  Online Content
4000 Post Club Member

Joined: Feb 2010
Posts: 4,339
Yup, there's nothing inherently easier about operations in base 10 over 8 or whatever except familiarity. Its dominance probably did come from finger counting.

#2122749 - 07/25/13 10:04 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: Dec 2009
Posts: 4,675
dewster Offline
4000 Post Club Member
dewster  Offline
4000 Post Club Member

Joined: Dec 2009
Posts: 4,675
Northern NJ
Base 2 works best for two state digital logic (which maximizes noise margins and allows for very high speed circuitry). This creates some conflict with our base 10 system because conversion between the two bases is necessary, and there are some exact decimals that form repeating decimals in the other system, thus hurting precision. I believe many older HP calculators performed internal operations in hexadecimal to avoid this.

The world of the digital designer would be a lot easier if we all went to base 4, 8, or 16 (my preference would be 16 because the binary width is 4 - a power of 2 - but that would make learning times tables more difficult for the little ones).

#2122777 - 07/25/13 11:19 AM Re: OT ... why base 10? [Re: rnaple]  
Joined: Jun 2013
Posts: 191
de cajon Offline
Full Member
de cajon  Offline
Full Member

Joined: Jun 2013
Posts: 191
London, UK
Originally Posted by rnaple
... of string theory. There are 11 strings. Less are incomplete. More are unstable.

I think there are many more than 11 strings if string theory is correct. However, said strings might vibrate in 11 dimensions crazy


Yamaha C3X SH
#2122854 - 07/25/13 02:11 PM Re: OT ... why base 10? [Re: rnaple]  
Joined: Aug 2009
Posts: 420
joflah Offline
Full Member
joflah  Offline
Full Member

Joined: Aug 2009
Posts: 420
St. Louis, MO, USA
Originally Posted by rnaple
I don't know why I mention this. Maybe I'm just stupid. From my very shallow knowledge of string theory. There are 11 strings. Less are incomplete. More are unstable. Here's where I probably fault....just off the top of my head... zero through ten make eleven. There is something special about eleven strings. Just something to think about.


Oh yeah! One-eighth of a piano.


Jack
#2123079 - 07/26/13 12:12 AM Re: OT ... why base 10? [Re: maurus]  
Joined: Nov 2012
Posts: 82
Schroeder II Offline
Full Member
Schroeder II  Offline
Full Member

Joined: Nov 2012
Posts: 82
Originally Posted by maurus
Interesting that you ask this question on a piano forum. Of course, for us the 10 fingers are crucial... wink

And yes, the main reason historically for a base 10 system seems to be the anatomical coincidence and the resulting practice of counting with fingers.

There were, and there are, alternative systems that have mathematical advantages. Some of them are also part of the modern baggage here ore there:

Systems with base 12 ('a dozen', 12 months, 2x12 hours a day, ...) have their advantages (they allow easy division by 2,3,4 and 6), and the Mesopotamian sexagesimal system with base 5x12=60 (even more easy divisors) was perhaps the best from a mathematical point of view. It is still at work in our measurement of time (an hour has 60 mins, a minute has 60 seconds) and of the circle (6x60 degrees, 1 degree = 60', 1'=60"...).

Some languages have remnants of a system with base 20 (see the French 'quatre-vingt' or Danish 'firsindstyve').

Otherwise, see the list linked above...

Circles actually have 360 degrees because until fairly modern times it was beliieved a year was 360 days long
Hence a day or 1 degree was 1/360 of that

Last edited by Schroeder II; 07/26/13 12:12 AM.
#2123133 - 07/26/13 01:52 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: May 2011
Posts: 1,247
maurus Offline
1000 Post Club Member
maurus  Offline
1000 Post Club Member

Joined: May 2011
Posts: 1,247
I am sorry, but this is nonsense. On the history of calendars see here.
There is a connection between measuring the circle, measuring time, and the calendar of course.

#2123219 - 07/26/13 08:49 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: Apr 2007
Posts: 3,540
gvfarns Offline
3000 Post Club Member
gvfarns  Offline
3000 Post Club Member

Joined: Apr 2007
Posts: 3,540
US
Not so fast.

According to the wikipedia entry on degree there are three theories for why there are 360 degrees in a circle (no one knows for sure).
  • In some early calendars (for example the Persian one) there were 360 days in a year
  • Babylonians used base 60 numbers so 6*60 was a natural choice
  • 360 is nicely divisible by lots of things

So I guess we don't really know but the calendar guess is as good as any.

#2123226 - 07/26/13 09:02 AM Re: OT ... why base 10? [Re: dewster]  
Joined: Aug 2009
Posts: 420
joflah Offline
Full Member
joflah  Offline
Full Member

Joined: Aug 2009
Posts: 420
St. Louis, MO, USA
Originally Posted by dewster
Base 2 works best for two state digital logic (which maximizes noise margins and allows for very high speed circuitry).


In effect, music uses binary fractions for note values, since all the subdivisions are powers of two.
whole note : 1
half note : 0.1
quarter : 0.01
eighth : 0.001
dotted eighth : 0.0011



Jack
#2123269 - 07/26/13 10:25 AM Re: OT ... why base 10? [Re: joflah]  
Joined: Aug 2010
Posts: 226
dje31 Offline
Full Member
dje31  Offline
Full Member

Joined: Aug 2010
Posts: 226
Originally Posted by joflah

In effect, music uses binary fractions for note values, since all the subdivisions are powers of two.
whole note : 1
half note : 0.1
quarter : 0.01
eighth : 0.001
dotted eighth : 0.0011



Wouldn't it be more accurate to say:

whole note : 1
half note : 0.5
quarter : 0.25
eighth : 0.125
dotted eighth : 0.1875

Not to be a complete math nerd...but I'm prepared to be...

Last edited by dje31; 07/26/13 10:27 AM.

Yamaha CP33 | Roland XP-30
#2123285 - 07/26/13 10:49 AM Re: OT ... why base 10? [Re: Dave Horne]  
Joined: Jun 2011
Posts: 4,145
PianoStudent88 Online content
4000 Post Club Member
PianoStudent88  Online Content
4000 Post Club Member

Joined: Jun 2011
Posts: 4,145
Maine
joflah was showing binary fractions, where the digits are 0 and 1 and each decimal place is 1/2 of the preceding place.

You are showing decimal fractions, where the digits are 0-9 and each decimal place is 1/12 of the preceding place..

joflah's point is that the binary fractions show a very simple pattern for the notes. To be a true math nerd: work out the binary fractions for triplets and for compound meter.


Piano Career Academy - Ilinca Vartic teaches the Russian school of piano playing
Musical-U - guidance for increasing musicality
Theta Music Trainer - fun ear training games
#2123349 - 07/26/13 01:01 PM Re: OT ... why base 10? [Re: PianoStudent88]  
Joined: Aug 2009
Posts: 420
joflah Offline
Full Member
joflah  Offline
Full Member

Joined: Aug 2009
Posts: 420
St. Louis, MO, USA
Originally Posted by PianoStudent88
joflah was showing binary fractions, where the digits are 0 and 1 and each decimal place is 1/2 of the preceding place.

You are showing decimal fractions, where the digits are 0-9 and each decimal place is 1/12 of the preceding place..

joflah's point is that the binary fractions show a very simple pattern for the notes. To be a true math nerd: work out the binary fractions for triplets and for compound meter.


Right.
But triplets would be a repeating expression-
triplet half note (in space of whole note): 0.01010101010... whereas in decimal, it'd be 0.33333...
You'd just have to show the division, same as in decimal: 1/11b for each of the three notes.
Compound meter? The notes would be the same, I guess.


Jack

Moderated by  Piano World 

Piano Acc. & Gift Items in
Piano World's Online Store
In PianoSupplies.com ,(a division of Piano World)
our online store for piano and music gifts and accessories, Digital Piano Dolly, party goods, tuning equipment, piano moving equipment, benches, lamps Caster Cups and more.


Free Shipping* on Jansen Artist Piano Benches, Cocoweb Piano Lamps, Hidrau Hydraulic Piano Benches
(*free shipping within contiguous U.S. only)
(ad)
Pearl River & Ritmuller
Ritmuller Pianos
(ad)
Pianoteq
PianoTeq 6 Out now
ad
Pierce Piano Atlas


New Topics - Multiple Forums
Key Top Replacement
by Mickey24. 12/12/17 05:18 PM
Certificates from Top Conservatories
by S'il Vous Plait. 12/12/17 02:05 PM
Amplifying synth through piano speakers?
by Paalrammer. 12/12/17 01:20 PM
Looking for some information, please!
by Mark Davis. 12/12/17 12:42 PM
Forum Statistics
Forums44
Topics183,244
Posts2,678,756
Members89,267
Most Online15,252
Mar 21st, 2010
(ad)
Accu-Tuner
Sanderson Accu-Tuner
Check It Out!
There's a lot more to Piano World than just the forums.
Click Here to
Explore The Rest of Piano World!!
Visit our online store for gifts for music lovers


 
Help keep the forums up and running with a donation, any amount is appreciated!
Or by becoming a Subscribing member! Thank-you.
Donate   Subscribe
 
Our Piano Related Classified Ads
| Dealers | Tuners | Lessons | Movers | Restorations | Pianos For Sale | Sell Your Piano |

Advertise on Piano World
| Subscribe | Piano World | PianoSupplies.com | Advertise on Piano World |
| |Contact | Privacy | Legal | About Us | Site Map | Free Newsletter |


copyright 1997 - 2017 Piano World ® all rights reserved
No part of this site may be reproduced without prior written permission
Powered by UBB.threads™ PHP Forum Software 7.6.0