My 'Temperament Systems' Article

Discussion in 'Miscellaneous [BG]' started by Jeff Moote, May 12, 2003.

  1. Jeff Moote

    Jeff Moote Supporting Member

    Oct 11, 2001
    Beamsville, ON, Canada
    Since temperament has been a topic of discussion around here before, I thought you might be interested in an article I did for physics on temperament systems. I realise some of it might not make sense to musician types who don't know sciences, as it's done from the physics perspective, but it should be somewhat useful.

    Hopefully someone gets something out of it (attached zipped in *.pdf form)

    Any feedback would be appreciated too.
  2. iplaybass

    iplaybass Guest

    Feb 13, 2000
    Germantown, TN
    I really enjoyed your article, it explained several things I never really understood, like how the octave was divided up and why some instruments are C instruments while others are different. I think the discussion of the systems in terms of music was a little weak, but since this is a physics paper I didn't expect a whole lot. I guess I'd like to read a little more about why the Pythagorean and Just Temperament systems sound better, and how harmonics and such are related to the division as such. Overall, a good piece of work... I think its strongest point is the fact that anyone, even one without a background in physics and harmonic motion, could understand it. Nice. :cool:
  3. Jeff Moote

    Jeff Moote Supporting Member

    Oct 11, 2001
    Beamsville, ON, Canada
    Thanks a great deal. This isn't really meant for musicians at all, and thus the second paragraph explains lots that any musician would assume to know, but it was for a Physics audience. This was a paper for my Gr. 11 Physics class, and I'm overall pretty happy. There's way more info to be had though, and I wish I would have had time to go into it.

    Anyone else's thoughts would be much appreciated.

    edit: for spelling
  4. geshel


    Oct 2, 2001
    As I read. . .

    - "Pythagorean Temperament uses the principles of the modes of resonance" -- you need to state resonance of what, as many objects (xylophone bars, bells, drums) don't have integer harmonics.

    - "there are two major faults in it that lead
    J.S. Bach to develop the Equally Tempered" -- that should be "led" , not "lead"

    - "the further from the initial key that the piece got, the more inaccurate the
    previous definitions of notes’ frequencies became." -- "further" is a somewhat vague term used like this. For instance, if you're just intoned to C, playing in C# will sound much worse than in G - so "further" doesn't literally mean in pitch offset. It probably gets worse as you travel the circle of fifths? Through G, D, A, E, etc. . . ?

    - "The Equally Temperament system was introduced to solve the aforementioned problems with Just Temperament, and simply divided the octave into semitones evenly." -- Maybe you could say "and simply divides the octave into 12 equal semitones". You've already mentioned above that the octave is divided into 12 semitones, but that the distance a semitone encompasses is not constant. The "evenly" doesn't seem clear enough to me to indicate that all the semitones are equal in 12tet (which brings me to. .. )

    - there are other Equal Tempered scales that don't use 12 tones - in fact as many as you want, you can have 10tet, 16tet, etc.

    "Since beat frequency is defined as:
    fB = | f2 - f1 |
    the lowest beat frequency of any one comparison that is audible is:
    fBmin = 0.05f1"

    This is not correct. f2 is 5 cents higher than f1, and so is 2^(5/1200), or 1.0029 times f1. Therefore fBmin is 0.0029f1.

    OK that should do ;). What level of school is this paper for?
  5. Mike Money

    Mike Money Banned

    Mar 18, 2003
    Bakersfield California
    Avatar Speakers Endorsing Hooligan
    To much reading.

    I got to the first chart, and that was damned cool.
  6. PollyBass

    PollyBass ******

    Jun 25, 2001
    Shreveport, LA
    OH YEAH? well....ugh....must,,,,,,hold back,,,,,mike,,,,,makes it to easy........must......control........must.........
  7. geshel


    Oct 2, 2001
    Polly, I only made it to the first ",,,,", sorry. Too much reading.
  8. geshel


    Oct 2, 2001
    Oh: and duh sorry Monty I see that it was for your 11th grade class. :)

    Nice job!
  9. pilotjones

    pilotjones Supporting Member

    Nov 8, 2001
    Nice introductory paper. It presents some of the math of music in a pretty clear manner.

    I agree with geshel's points. And yes, "further away" is actually further around the circle of fifths, not distance along the scale- although you would then have to explain what a circle of fifths is.

    Good job.
  10. Jeff Moote

    Jeff Moote Supporting Member

    Oct 11, 2001
    Beamsville, ON, Canada
    Thanks for the feedback folks.

    Thanks. Of the issues you mentioned, I was aware of all of them (but didn't want to bother to explain the circle of fifths (it's a science paper anyway)) but just didn't fix them after I had already completed it. I left things like equally tempered systems with 10/16/whatever tones just for simplicity. It was supposed to be about 500 words anyway, and that was 3000. I could have gone on much longer.

    That said, thanks greatly for the suggestions. Do you think that's appropriate for my level?

    As I said, I knew that it was the circle of fifths that is pertainant, but I didn't want to explain that. I'm glad it was effective in explaining this aspect of music at this level... that was the intention.
  11. geshel


    Oct 2, 2001
    Appropriate? Beats me. :) Based on my high school science memories, it seems fairly advanced - though we didn't have the most advanced science curriculum.
  12. Jeff Moote

    Jeff Moote Supporting Member

    Oct 11, 2001
    Beamsville, ON, Canada
    Heh, ok, thanks. Yeah, I dunno... it was way beyond what was intended really, but I enjoy it.

    Hmm... I suppose I'm getting further along my way to a science degree. Only a year and a few months more of HS :smug: