Mathy revelation

[Allan Haley]

Hi steelers.

I was practicing harmonized scales this morning and hit on a mathy connection between the tunings of some pairs of strings.

The 3 and 4 strings are tuned the same as the 6 and 8 strings- both being G# and E, respectively. Interestingly, 3/4 and 6/8 are equivalent fractions.

The same is true with strings 4 and 5 and strings 8 and 10. Both pairs are tuned E and B, respectively. 4/5 and 8/10 also are equivalent fractions.

I think I will find this helpful as I struggle to get more comfortable playing this instrument- it certainly appeals to the math nerd in me.

Al

[Ian Rae]

I think I will find this helpful

Clearly you will. It's a shame that there's no deep significance in it, as string 4 was string 2 before Buddy Emmons, and string 1 before Ralph Mooney.

But finding patterns is what separates men from beasts (and mathematicians from mere men)

[John Goux]

I'd noticed that, too. I wondered whether the architects of our E9 tuning were aware of this, and had planned the tuning with this in mind.
For an added math angle...the frequencies of our higher octaves strings, in Hz, are double that of the lower. Similar to 3-6, 4-8, 5-10. Don't ask me the frequencies, but I think octaves are twice the Hz.
J

[Jeremy Threlfall]

http://www.phy.mtu.edu/~suits/notefreqs.html

[Ian Rae]

I wondered whether the architects of our E9 tuning were aware of this, and had planned the tuning with this in mind.

Sorry to disappoint, but the string numbers are arbitrary and depend how many strings are on the guitar. But you're quite right about an octave being a doubling of frequency. Most musical cultures - even the ones that don't have scales - recognise this 2:1 ratio as meaningful, and the other relationships between notes which we regard as building blocks are based on simple fractions (3rd = 5:4, 4th = 4:3, 5th = 3:2, 6th = 5:3 etc.) although in practice they are usually modified to the values in Jeremy's chart for reasons which have been elaborated many times on here.

[Tim Russell]

I'm not sure if I would read too much into the 3/4 - 6/8 string relation...sometimes things just work out as coincidence. That being said, music is definitely purely mathematically based.

I have always been intrigued by the use of math/time signatures employed by the band "Rush" - one of their most famous pieces being "Y-Y-Z" that is completely based on math/numbers, played in a time signature of 5/4.

I used to have a site bookmarked that explained the whole YYZ thing in detail, but I cannot seem to locate it at the moment. It is a very interesting read for math nerds, lol.

[Ian Rae]

I am sceptical of too much mathematics being injected artificially into music, like a hormone.

When we hear something pleasing, the explanation is mathematical, but just because something is heavy on the math doesn't mean it sounds musical at all.

A lot of 20th concert music was conceived by numbers, but the inner workings are lost on the human ear.

[Michael Hummel]

I don't know EVERYTHING about Rush nor YYZ, but here's a few things I CAN tell you:

1. I grew up in Willowdale (Toronto) 4 blocks from Geddy Lee and Alex Lifeson

2. (C)YYZ is the international aeronautical designation for the Toronto Pearson International Airport

3. The Morse code for the letters Y-Y-Z is -.-- -.-- --.. and you can hear the band play this pattern over a 5/4 time signature

4. I was lucky to have Rush play at my high school a few times 40 years ago (before Neil Peart, but Alex Lifeson had a lifelong effect on my guitar playing)

Cheers,
Mike