Number patterns in different bases

[pgrmdave]

Are there any patterns in numbers that occur only in different number systems - binary, or hexadecimal and the like?

[Turtle]

Inddeed! On my page under Pictures are graphs of just exactly what you asked. In addition, if you write 22/7 (approx. pi) in base twelve & divide, you arrive at a repeating decimal. Now when I work in base twelve, J is the number 10 & K is eleven.
http://home.comcast.net/~turtlediable/wsb/index.html

[BlameTheEx]

Turtle J and k ????

As an assembler programer I often used hexadecimal (base 16) the count went 123456789ABCDEF. I have to admit I never found a professional reason to use base 12. Is J and K a standard?

Base 12 is the perfect base. Music notation is a dodle in base 12. as many a shopkeeper has discovered 12 items are easy to pack or divide up.

Humanity had its chance to go for base 12 and flunked it. We have the dozens and the gross. before we went metric here in the UK we has 12 pennies to the shilling. Sigh.

[Turtle]

It's no standard;except with turtles. I mean let's be logical about it; J is the 10th letter of the alphabet, K the eleventh. I would even use A for 1 on up but for familiaritie's sake. As to why use other bases? Why for exploration of course. One has to find a thing before deciding if such a thing is useful. I go where angels fear to tread. Come along!

[BlameTheEx]

Tuttle
Keep up the good work.

However I suspect it might be better to use A and B for communication to others. Hexadecimal is the only base greater than 10 in common use (at least on this planet). Best to follow its conventions.

Edit: Wait a moment. duodecimal IS in common use, in musical notation. Frankly however I have no wish to promote: C,Db,D,Eb,E,F,Gb,G,Ab,A,Bb,B

[Tormod]

Originally Posted by BlameTheEx

Edit: Wait a moment. duodecimal IS in common use, in musical notation. Frankly however I have no wish to promote: C,Db,D,Eb,E,F,Gb,G,Ab,A,Bb,B

I do. And don't forget Cb, C#, Db#, E#, Fb, F#, G#, A#, B#...not to mention the double ## and bb's.

[BlameTheEx]

Tormod

Lol. I suspect I didn't get the scale right, but I am absolutely sure you didn't.

There are no double ## and bb's. Db# if it had any meaning at all would be the same as D. There are only 5 sharps or flats, and each one can be accurately described as a sharp OR a flat, but using both is like demanding a slice of cake under your surname and a second slice using your christian name.

All this proves my point. The music scale is not as easy to comprehend as could be wished. This is because it evolved from a 7 note music scale. Just another example as to how history complicates things.

Had musical notation been newly invented now, I have no doubt that the notation would be 0,1,2,3,4,5,6,7,8,9,A,B. Perhaps it is a good thing our distant ancestors are dead. If they were not I would be tempted to kill them.

Edit

For more information on the topic of musical scales and malicious impulses, please watch "The 5000 fingers of doctor T"

[Tormod]

Blame, I studied music for 4 years (I'm a Bachelor of Music in Performance) and have played since I was 6.

There are indeed double sharps and flats. Consider this - if you are playing a piece in the key of C# and play an augmented 5th chord, you get the following notes: C#, E#, G## (usually notated as Gx).

The same goes for a minor scale in Cb - you'd get a minor third which gives you an Ebb (E flat flat).

You could also easily get a Db#. It wouldn't be notated as such, because the key is notated at the clef and not with each note, but still. Consider this - if you play in the key of Eb minor and play a melodic minor scale, you'd get a Db# going up towards the Eb, and a regular Db going back down.

It is incorrect to state that flats are the same as sharps. For all PRACTICAL purposes they sound the same to us, which is why most instruments today use the same key/valve/fret, but they are not. At my old college we had a church organ with (yup) TWO black keys for each regular black key - one for the sharp and one for the flat note.

Still, I'd say the western music scale is astonishingly simple. 13 notes. No matter where you start or end, there are only 13 notes in an octave (counting the octave).

But I heartily agree - it's a good thing we don't write our essays in the key of C double sharp.

[Tormod]

I should add that anyone who tried to play the organ at Augustana College probably never tried it again.

[Tormod]

BTW, a source for you about double sharps:

http://www.music.vt.edu/musicdiction...ublesharp.html