h a l f b a k e r yWarm and Fussy
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Prime numbers are those divisible only by themselves and one and are regarded as beautiful by pure mathematicians. There are no discovered patterns to the dispersal of prime numbers within number sets and indeed, for all our advances, there are no formulas to predict the next prime number.
Within
an octave of 8 notes, 5 of these notes are prime. Within the key of C, the notes C, D, E, G, A and B [notes 1, 2, 3, 5, 7 within the octave] are prime.
I propose musical pieces composed only using prime notes : Prime Melodies. The chords and melodies available will have a mathematical beauty about them. Extra emphasis on chords such as CMaj7th should be used as it employs the 1, 3, 5, 7 of the key. It's a prime chord.
For the piano player : A full size piano keyboard has 88 keys : some of these notes are prime [1, 2, 3, 5, 7, 11 … 79, 83]. Prime piano concertos using only prime notes.
(?) The Circle of Fifths
http://www.mikemurp...essons/lesson18.htm
Not really related but interesting for those who want to learn more about music. [bristolz, Oct 04 2004, last modified Oct 21 2004]
Prime numbers and music.
http://home22.inet....sic_and_numbers.htm
Prime interval (perfect fifth) mentioned. [bristolz, Oct 04 2004, last modified Oct 21 2004]
(?) Prime listening
http://www.maa.org/...thtrek_6_22_98.html
"Mathematician Chris K. Caldwell of the University of Tennessee in Martin has developed a scheme for listening to sequences of primes--to hear both simple patterns and perplexing irregularities found among those numbers." [bristolz, Oct 04 2004, last modified Oct 21 2004]
(?) The Musical Scale
http://www.hypermat...oc/other/musint.htm
Scales and intervals explored with a mathematical flavor. [bristolz, Oct 04 2004, last modified Oct 21 2004]
computational music
http://tones.wolfram.com
niftylittle computational universe that creates math music of various genres that you can download as a ringtone [bleh, May 31 2006]
ZynAddSubFX
http://zynaddsubfx.sourceforge.net/
[spidermother, Jun 01 2006]
[link]
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I wonder if some Eastern modes, which use different scales than our usual Western mode, would qualify for this? I suspect pieces of music exist which qualify, but probably not composed deliberately. Nice. Wonder what it sounds like? Mathematicians apparently make very good musicians... |
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I think it's the other way 'round. |
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Is that decimalize, or decimate? |
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Bumper sticker:
Honk the Fibonacci series if you
love algorithmic music. |
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I know the rule of thumb for punk music is the "rule of 3" ... only use 3 chords ... |
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// uneven staggering and to have a nicer amount of divisions than the present ... // |
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Every note is separated from its neighbour* in frequency by exactly the twelfth root of 2. |
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Therefore, the same note in the next octave up or down is double or half the frequency of the original. The things we learn in high school physics ;) |
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Oh, look, [bristolz] posted a link. :P |
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--
*Flats and sharps are considered neighbours to the original. |
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a friend of mine did a study on the fibonacci numbers in highschool and found that most composed music (classical) fit into them in some fasion. |
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she was a first chair violin player, very very talented.
and dang smart. |
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That is an interesting topic: Say I just made a new composition using my emotional intellect and someone says "That sounds nice." I could also make the same piece ,then I say I did it using the phone book someone says "Oh. Why." |
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The prime numbers are only beautiful and pure because they're infinite. Once you bound them above and below, they cease to be beautiful and instead form a random collection of notes. |
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Music is always bounded, because the human ear can only hear notes within a certain range. |
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To make this clear, why should the primes beginning at "do" (1,2,3,5,and 7 tones) be used? Why not the primes counting downward from the top of the scale (8, 7, 6, 3, 1) ? |
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Also, since the scale is logarithmic in nature, what interaction is there between primes and logarithmic frequencies? |
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If you wish to create music of prime proportion, I believe you need to recreate the scale from scratch. The frequencies of vibration themselves need to be calibrated so as to be in prime-number proportion to each other. |
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And you know what? After you do that, it would probably sound horrible. |
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[phundug] Actually, such prime number proportions of frequency are very beautiful and provide some of the richest grounds for musical exploration. Intervals based on 2, 3, and 5 form the basis of most western music. 7 produces a lovely bluesy sound and is found in some African and Middle Eastern music. Beyond that, things get interesting, but to my ear, even up to about 23 the harmonies are more pleasing than, for example, an equal-temperament major 3rd. Beyond that it gets a bit harder to hear the harmony. |
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most western music already does this. chord tones are 1-3-5&7 . the 2 is often written as a 9th (an octave up) all of which are very common in our music. Jazz music generally has a 2-5-1 chord progression. I agree with phun that a new scale may need to be written to truly achieve this idea, but it would likely be so abstract that it would be more art for the sake of math than really beautiful. maybe you could get into addition and subtraction tones of prime intervals to get even more interesting tones. |
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see link for interesting computational music. |
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also- the cycling pulses of neighboring notes contain a some mathmatical interest. if you have a keyboard, go to a sin wavesound and play c, c# and d# in the lowest octave and listen to the cycling pulses created, more tones, more pulses, longer cycles. |
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[bleh] <picky> These notes (c, c# and d#) relate as 1 : 2^(1/12) : 2^(1/4), so the pattern of pulses never cycles, which is part of the interest. </picky> |
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Whether you have a keyboard or not, you can download ZynAddSubFX (link), click on scales, click the 'Enable Microtonal' box, then start replacing the numbers under 'tunings' with prime numbers and ratios of prime numbers, eg 3, 7/5. Then you get patterns that do cycle, at a frequency equal to the lowest common denominator of the frequencies played, creating harmony at high frequencies and intricate rhythmic pulses, like African or Indonesian compound rhythms, at low frequencies. Play the results with the virtual keyboard under the Instrument menu or hook up a sequencer or external keyboard. |
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I think these scales really are beautiful; they relate directly to the harmonic series, which our hearing systems seem to delight in. Each new prime introduces a new type of harmony, to a greater extent than composites of primes already heard (much as the qualitative difference between a major 3rd and a perfect fifth is greater than the difference between a major 6th and a major 3rd, and for precisely the same reason), so this is far less arbitrary than selecting prime notes from an existing scale. |
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//the scale is logarithmic in nature// err.. sort of, not really, actually no. The qualitative sensation of pitch is related to the logarithm of frequency, which is why the geometric series of frequencies in an equal temperament sounds like a linear increase in pitch (eg all semitones on a piano are percieved as being the same size). Besides, harmonic scales are twice the 'the' geometric scales ever were. Of course, I now have to go and generate some logarithmic scales, just to be perverse. |
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The idea gets a plus, mostly for giving me a chance to rant on one of my favourite topics :-) |
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How about only playing notes of Hz that are real prime numbers? |
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That would likely lead to some seriously ugly music.. and probably not much more. |
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