pgrmdave Posted January 24, 2005 Report Share Posted January 24, 2005 Are there any patterns in numbers that occur only in different number systems - binary, or hexadecimal and the like? Link to comment Share on other sites More sharing options...
Turtle Posted January 24, 2005 Report Share Posted January 24, 2005 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 ;) Link to comment Share on other sites More sharing options...
BlameTheEx Posted January 24, 2005 Report Share Posted January 24, 2005 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. Link to comment Share on other sites More sharing options...
Turtle Posted January 24, 2005 Report Share Posted January 24, 2005 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! ;) Link to comment Share on other sites More sharing options...
BlameTheEx Posted January 25, 2005 Report Share Posted January 25, 2005 TuttleKeep 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 Link to comment Share on other sites More sharing options...
Tormod Posted January 25, 2005 Report Share Posted January 25, 2005 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. ;) Link to comment Share on other sites More sharing options...
BlameTheEx Posted January 25, 2005 Report Share Posted January 25, 2005 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" Link to comment Share on other sites More sharing options...
Tormod Posted January 25, 2005 Report Share Posted January 25, 2005 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. ;) Link to comment Share on other sites More sharing options...
Tormod Posted January 25, 2005 Report Share Posted January 25, 2005 I should add that anyone who tried to play the organ at Augustana College probably never tried it again. ;) Link to comment Share on other sites More sharing options...
Tormod Posted January 25, 2005 Report Share Posted January 25, 2005 BTW, a source for you about double sharps: http://www.music.vt.edu/musicdictionary/textd/Doublesharp.html Link to comment Share on other sites More sharing options...
Tormod Posted January 25, 2005 Report Share Posted January 25, 2005 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. Actually, I'm not doing this part entirely correct. A Db# would be notated with the "natural" sign which overrules the flat. So the Db# does not exist - it would be a naturalized Db (which, as you write, sounds like a D). But the concept remains - it is the key which decides whether you need single or double flats or sharps. ;) Link to comment Share on other sites More sharing options...
BlameTheEx Posted January 25, 2005 Report Share Posted January 25, 2005 Tormod Damn. You got me. I was thinking no further than the even tempered scale. I concede that if you insist on a diatonic scale, playable in any key, things get complicated very fast. In theory there is no limit to the mess you can get into. You play a note. You then play a correct diatonic harmonic of that note (which is a little different from the even tempered key). Now you play the same diatonic harmonic of the new note and so on. It is possible to drift further away from the even tempered scale with each note. In theory it should be possible write notation describing this drift, but I would hate to see what it would look like! Link to comment Share on other sites More sharing options...
pgrmdave Posted January 25, 2005 Author Report Share Posted January 25, 2005 It gets more complicated when you take into account all the different tuning systems. And that's just in Western music. Link to comment Share on other sites More sharing options...
Turtle Posted January 25, 2005 Report Share Posted January 25, 2005 Yes I know the convention, but I do work in other bases & do so unconventially. If you looked at the tables under Pictures on my page:http://home.comcast.net/~turtlediable/wsb/index.htmlyou see I have adopted the disonvention of using color for numbers!. I haven't put up the key yet but 1 is black, 2 is red, 3 orange, 4 yellow... Well, for the multiplication tables you can take the key from the top row or left column. Yes, I used J=10, K=L. 10 = metallic black, 11 = metallic red. Tormod, I invite you to musicalize my graphs! I have many others not posted so if you get a feel for them & an idea that some certain base you want let me know. ;) ;) Link to comment Share on other sites More sharing options...
Tormod Posted January 26, 2005 Report Share Posted January 26, 2005 I can only say "Wow!" and enjoy your beautiful drawings until I find some way to understand them...is there some way you can give me any hints as to how I should interpret these? I'd love to try to make a musical piece or something based upon this. Link to comment Share on other sites More sharing options...
Turtle Posted January 27, 2005 Report Share Posted January 27, 2005 No hints! Instead, I will explain exactly what they are if you allow me some time & lattitude. I call this Katabatak math & it is my own exploration in what most comfortably you can call pure math. I borrow freely from many areas of math, I coin some of my own terms, I make conjectures without proof, & you may have to stand on your head outside the box to see my view. I have spent a decade on this & my aim with your help is to simply present what I found. Shall we begin? Do we have an understanding? ;) Link to comment Share on other sites More sharing options...
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