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Chart for frequency and notes
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Joined: Wed Jan 16, 2013 2:33 am
Posts: 165
Chart for frequency and notes

http://en.wikipedia.org/wiki/Note#Note_ ... 28hertz.29

This chart may come in handy some day when it comes time to develop music for your SBC.

Tue Jan 22, 2013 5:56 am

Joined: Tue Dec 11, 2012 3:41 am
Posts: 68
A nice feature about notes is that their frequencies can be exactly calculated with a exponential formula! I was surprised when I discovered that, music is math!
Here is another link that i found a while ago:
http://www.phys.unsw.edu.au/jw/notes.html

Tue Jan 22, 2013 7:47 pm

Joined: Tue Dec 11, 2012 8:03 am
Posts: 285
Location: California
Then there's the difference between even-tempered and well-tempered which I as a cellist (the cello having no frets) am always dealing with. For example "perfect 5ths" are not really perfect, as an even-temered scale gives a ratio of 2^(7/12)=1.498 which is slightly below the well-tempered version, 1.500, and the third in an even-tempered scale gives a ratio of 2^(4/12)=1.260 which is slightly above the 1.250 of the well-tempered version. For tuning most instruments, we go with even-tempered, ie, powers of the twelvth root of two, since it is the best compromise for dealing with all keys.

Wire gauge is also a log function, and every three numbers doubles the diameter of the wire. I keep the function and inverse funcion in my HP-41cx calculator so I don't have to look them up from a table.
AWG = -ln(diam)*8.628 - 9.71
Diam = 2.0045^(-(AWG+9.71)/6)
(Diameter is in inches.) This is my own curve fit from the tables.

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Tue Jan 22, 2013 8:56 pm

Joined: Tue Jan 15, 2013 10:11 am
Posts: 114
Location: Norway/Japan
(Ah, I'm replying to Dajgoro's post - I noticed that Garth posted in the meantime)

There's always been a connection between music and math.. it's just that equal temperament, the modern Western scale, is calculated a bit differently than the natural, Pythagorean scale. Otherwise you would be stuck with a selection of about five tones for chord-based music (music with more than one tone played together). The equal temperament scale is based on logarithms, but the "natural" scale is firmly based on fractions: All the notes of a scale can be calculated from fractions of the base note, up to the octave which is of course twice the frequency (and is the one that is the same in equal temperament). In other words, in the natural scale all notes are based on true harmonics of the base note, this is not the case for equal temperament (except the octave), there's a small error which can be heard, but it does make it possible to play all the chords we want to without it sounding too bad.

The problem with the natural scale is that when you calculate harmonics from the base note (as in 1/2, 1/3, 1/5 and so on of the base note) you will end up with slightly different notes when you start calculating notes that way from the _second_ note of the scale.. that's why a guitar will sound bad when people try to tune it by using harmonics at the fifth and seventh frets, a typical mistake. One chord sounds good, the next one sounds really bad. You just can't tune a fretted instrument like a guitar (or a piano) using the natural scale - you would only be able to play very limited variants of five-tone (pentatonic) music.

Equal temperament, or natural.. it's all math, even so.. and when some people argue that music is invented, not discovered, because Eastern music, for example, has many more notes than the Western 12 notes, they're wrong: The reason they have more notes is simply that they use more of the Pythagorean fractions than Western music does, so there are more notes to choose from. It's just more of the same. So in my opinion music _is_ something that was discovered, not invented, or at least as much discovered as math was discovered (and that discussion won't ever finish either..)

Finally there's the theory that there are slightly more amateur musicians among programmers and mathematicians than in the general population. I've had reason to believe in that for the most part, but I once worked in a place where there were none.. except myself and two others, and all three of us were contracted from elsewhere. I admit that was unexpected.

-Tor

Tue Jan 22, 2013 9:19 pm

Joined: Tue Dec 11, 2012 3:41 am
Posts: 68
Quote:
Finally there's the theory that there are slightly more amateur musicians among programmers and mathematicians than in the general population.

That explains why there is a band hiding in a local hackerspace here in Zagreb...

As for the rest, I am not a musician, I like music, but I don't know how to play any instrument. So most of that what you wrote wasn't very clear to me.

Tue Jan 22, 2013 11:29 pm

Joined: Tue Jan 15, 2013 5:43 am
Posts: 184
Tor wrote:
You just can't tune a fretted instrument like a guitar (or a piano) using the natural scale
Right. Fretlessness is next to godliness, I say!

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Wed Jan 23, 2013 5:14 am

Joined: Tue Jan 15, 2013 4:15 am
Posts: 4
Dajgoro wrote:
As for the rest, I am not a musician, I like music, but I don't know how to play any instrument. So most of that what you wrote wasn't very clear to me.

It was a nice technical discussion about notes and frequencies.

But I, too, am musically challenged (I can't play the radio...).

As I get in to discussion with my music geek friends and they can detect my (remote) baffled confusions, my one friend likes to quip: "Talking about music is like dancing about architecture." Kind of need to hear it in situ with the discussion to grok it better . This is difficult to do over instant messaging.

Wed Jan 23, 2013 9:35 pm

Joined: Tue Jan 15, 2013 5:43 am
Posts: 184
Quote:
It was a nice technical discussion about notes and frequencies.

But I, too, am musically challenged

Not to worry -- we don't need to fully explore the details. Even for musicians the difference between even-tempered and well-tempered scales is very often immaterial. As Garth says, "For tuning most instruments, we go with even-tempered, ie, powers of the twelvth root of two, since it is the best compromise for dealing with all keys." Though theoretically imperfect, this compromise is highly acceptable, and to a large extent it renders the temperament question a non-issue. By no means is it a learning curve that every musician must master!

Reference was made to frets, as found on instruments such as guitar and lute. These are a means to quantize the frequency of the individual notes that are made available. Other stringed instruments do not have frets, for example members of the violin family (violin, viola, cello and double bass), the oud, and some electric bass guitars. With fretless instruments the frequency produced is an analog function of the player's finger position along the string. The absence of frets/quantization means that any intermediate frequency can be produced. Frets are both a convenience and a limitation. Now, back to electronics and computers!

When electronic pianos and other keyboard instruments became consumer items in the 20th century, most products used a "Top Octave Generator" IC to produce the 12 frequencies of the scale. An example is the MK50240, whose block diagram I'm including below. Such ICs were available from an assortment of manufacturers, and they varied in how accurately they approximated the frequencies of an even-tempered scale. Not surprisingly, the best results require the most silicon. The MK50240 begins with a master clock far in the ultrasonic (>2 MHz) and applies divide ratios ranging from 239 to 451. You can google "top octave generator" if you're curious about alternative formulas -- for example, as Chuckt says, "when it comes time to develop music for your SBC."

cheers
Jeff

http://LaughtonElectronics.com
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Sat Jan 26, 2013 2:39 am
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