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New Music Notes

They say that music is mathematical, so...
 
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How about playing the square root of E-flat, or the sine of Middle C, or the natural logarithm of B-sharp, or ....

:)

Vernon, Apr 21 2004

Frequencies and wavelengths for musical notes http://www.phy.mtu....uits/notefreqs.html
Equal temperment. [bristolz, Oct 21 2004]

The offset between equal and just temperment http://www.phy.mtu.edu/~suits/scales.html
Along with a cursory description of temperment and why there are different tunings and stringing scales. [bristolz, Oct 21 2004]

[link]






       Using frequency or wavelength or what as the number associated with the note?
bristolz, Apr 21 2004
  

       I like it. And easy enough to implement, I think.
ldischler, Apr 21 2004
  

       //sine of middle C// Is that in degrees or radians?
yabba do yabba dabba, Apr 21 2004
  

       [bristolz], frequency and wavelength are really the only two choices. Both are numbers. Thus, to maximize the quantity of new notes, figure it both ways!   

       [yabba...], again, feel free to do it both ways!
Vernon, Apr 21 2004
  

       Are we talking about new melodies or new notations for existing melodies expressed mathematically?
theircompetitor, Apr 21 2004
  

       Well, no, that's not true [Vernon]. There are numerical labels for all of the notes on, say, a piano compass or one could create their own numbering scheme. Vernotation, maybe.
bristolz, Apr 21 2004
  

       TC, methinks the latter would sound quite awful.
yabba do yabba dabba, Apr 21 2004
  

       wait, yabba, I think you mean the former, since the latter would be existing music?
theircompetitor, Apr 21 2004
  

       [bristolz], OK, I grant that units of time (used in frequency numbers) and length (used in wavelength numbers) are arbitrary. Still, Physics has offered us a couple things that might qualify as Universe-Wide Standards (the "Planck Time" and the "Planck Length" are literally supposed to be fundamental quanta of those units). All other measurement-units can be considered mere multiples (33 or more "orders of magnitude"!) of those fundamental units. So, pick some particular multiplier, and call the results "standard units" on the human scale (like the "second" and the "centimeter"). Then see how known musical notes are described in those units...and THEN have fun with square roots, sines, logarithms, etc.   

       Really, I just threw this Idea out more for its entertainment value, than for anything else.
Vernon, Apr 21 2004
  

       ...sorry, tc. I read the latter as transforming existing music to such a scale. The former may or may not sound awful--if you spent enough time experimenting, you could probably get some good sounds from it.
yabba do yabba dabba, Apr 21 2004
  

       I'm probably being obvious here, but when music is digitized it is already expressed in a mathematical notation.
theircompetitor, Apr 21 2004
  

       Yeah. The idea is to transform the music using some mathematical standard--use whatever notation you want.
yabba do yabba dabba, Apr 21 2004
  

       D'oh! (a D'eer)
bristolz, Apr 21 2004
  

       Read a very interesting article by Bob Moog about the mathematics of calculating the perfect third once.   

       Yeah, long done, old stuff this.
waugsqueke, Apr 21 2004
  

       Folks, this idea is actually not really about "transforming" music. I was actually just thinking about adding MORE notes to the standard repertoire. I was also just having some fun: the more off-the-wall these new notes, the better.
Vernon, Apr 22 2004
  

       adding more notes means that you'll end up with notes between those we currently have.   

       A is 440Hz. Your idea may mean that a note is created at 435Hz. This will indeed expand the palette of notes available to a more Eastern range.   

       Sadly though, many listeners may just feel that the music is flat or sharp.
jonthegeologist, Apr 22 2004
  

       Sadly? Why?
yabba do yabba dabba, Apr 22 2004
  

       These notes already exist. How about entering a math problem into a computer and have the computer express the solution melodically? Or how about assigning numbers to colors, and have the computer depict the solution both graphically and melodically?
simple123, Apr 22 2004
  

       [simple123], yes, in a manner of speaking, every note that can exist is already potentially available. But standard music notation only covers a certain incrementation of notes, thereby leaving out an infinity of others.   

       So, imagine a music-score sheet, in which here and there, a given note was specified inside a square-root symbol, for example....
Vernon, Apr 22 2004
  

      
thumbwax, Apr 22 2004
  

       [half], the IDEA for such notes has to be accepted, before you can go and expect others to understand modified notation!
Vernon, Apr 22 2004
  

       <wondering> The notes would need to sound "pleasing", when played with each other, otherwise who would listen?. So what makes existing sequences sound pleasing? Are there other ways apart from dividing an octave into 12 notes, and using 12th root of 2 function?<wondering>

Later: found there are many ways. The most pleasing seems to be where there are certain ratios betweeen frequencies i.e. (4:5), (5:6). The problem comes when shifting key, and with 12 divisions of an octave it is impossible to preserve the correct ratio in every case.
Ling, Apr 22 2004
  

       Watch out kids.   

       This is what happens when mathematicians fail to see the world in non-mathematical terms.   

       Of course all these notes already exist. How else would you account for note-bending or vibrato?   

       JS Bach really understood the maths of music, apparently, and wrote e.g. his preludes and fugues to explore it.   

       Apparently, if you were to play a note on a string, play the octave higher, and continue to do that up to eight octaves above the original note, the note that you reach will be one eighth of a tone flatter than the true note ought to be.   

       Can anyone confirm this for me, please?   

       If so, it will be the most useless fact I know. If not, I will continue to pass it off as fact.
lemon tetra, Apr 23 2004
  

       If your instrument is tuned using equal temperament, this won't be the case.
yabba do yabba dabba, Apr 23 2004
  

       After quickly checking - the temperaments that I saw had one thing in common: the octaves were the same frequency (i.e. doubling each time). The difference is in the frequency of the semitones in between. There is perhaps 10% of a semitone "error" in some cases.
Ling, Apr 23 2004
  

       //There is perhaps 10% of a semitone "error" in some cases.//
Well yes; that's the reason for the different systems of temperament - to divide the error and put it in places where it causes least offence.
"The last good thing written in C++ was Pachelbel's Canon."
angel, Apr 23 2004
  

       You want some funky music? Try replacing all half-steps with whole steps! (All other intervals remain the same).   

       Thus, "Twinkle Twinkle Little Star" would be:
C C G G A A G
F F Eb Eb C# C# B
F# F# E E D D C,
G G F F Eb Eb C#,
B B F# F# G# G# F#,
E E D D C C Bb.
phundug, Apr 23 2004
  

       Disgusting, phundug. Although whole-tone scales have their place in music. (paranoid android)
yabba do yabba dabba, Apr 23 2004
  

       BTW, many birds sing in a tonality that is not based on twelfth-roots of 2. Birds use other roots such as 10th or 11th, and their base multiple is 3. This is why birds' songs don't correspond with notes that you can play on a piano.   

       However, certain species, notable Baltimore Orioles and White-Crowned sparrows, *do* amaze me by always singing in actual musical tunes, playable using the 12 tones on a piano. These species must have 12 as their root and 2 as their diapason multiple.
phundug, Apr 23 2004
  

       Do you have a link for that?
yabba do yabba dabba, Apr 23 2004
  

       [angel], you are tempting me with puns about software (C++).
Ling, Apr 23 2004
  

       [yabba] No link; it's my own theory.
phundug, Apr 23 2004
  

       Seems like without extensive testing, you can't really say anything more than "birds of differing species use different systems."
yabba do yabba dabba, Apr 23 2004
  

       I suppose that you could squeeze quarter tone intervals between the half tones but eventually you would sound more like you are out of tune than actually playing a real note.
Jscotty, Sep 29 2005
  

       Quarter-tones are common in Eastern music, and were used (to dubious effect, depending on your heritage) in 'Zero Time', by Tonto's Expanding Head Band.
angel, Sep 29 2005
  
      
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