# Thread: Greek letter symbol for 12th root of 2

1. ## Greek letter symbol for 12th root of 2

In an equally tempered musical scale, the ratio between adjacent notes is the 12th root of 2 ( 1.059... ).
As far as I have been able to find, this value has never been represented by a greek letter.

I am using phi to represent this value as it has been used to represent a ratio, the golden ratio, and it
is a ratio that I am trying to represent.

Is phi a bad choice because of it's being already used for a different ratio value?

Is there a better choice?

2. phi is used to represent many different things, as long as you tell someone that phi is the 12th root of 2, what does it matter?

3. Ok, thanks.

Phi it is then.

I was worried about the fact that phi was already being used for a constant, 1.618..., the golden ratio.

4. A musician guy, said to take a look here.

5. The Dimensionless quantity lists a lot of common dimensionless quantities. Perhaps uppercase delta,
Δ = 21/12 ≈ 1.0594630943592952645618252949463417
would be better? I'm not saying φ is a bad choice, though -- unless, of course, you have to mention the golden ratio in the same text.

6. O_o

Have you considered any of the archaic variations?

They would still be a Greek letter, but they are largely unused.

Soma

7. Originally Posted by phantomotap
O_o

Have you considered any of the archaic variations?

They would still be a Greek letter, but they are largely unused.

Soma
No, and mainly because I am unfamiliar with them. Also, the common greek letters have very diversified uses
and it seemed there ought to be a good choice among them.

I was surprised to see how many of the greek letters have specific representations; I looked through them here:

Greek letters used in mathematics, science, and engineering - Wikipedia, the free encyclopedia

I had assumed that each one was typically used for certain types of values.

Originally Posted by Nominal Animal
The Dimensionless

quantity
lists a lot of common dimensionless quantities. Perhaps uppercase delta,
Δ = 21/12 ≈ 1.0594630943592952645618252949463417
would be better? I'm not saying φ is a bad choice, though -- unless, of course, you have to mention the golden ratio in

the same text.
I wanted to avoid any that I already commonly use, like delta for a difference or change, or alpha for a coefficient.
There's little chance that the golden ratio will show up along with 12th root of 2 in my programs. But it does have
that representation, so I was wondering about it. For example, pi would be a really bad choice.

Originally Posted by std10093
A musician guy, said to take a look

here.
Lot of information there. But I don't see any reference to a symbol or name for the 12th root of 2.

Possibly it does have an "official" symbol or name in the musical instrument industry. Music keyboard makers must have
to deal with the value in their software.

8. Well, to be honest, does 21/12 = 12√2̅ need a separate symbol?

The Latin-1 supplement (that includes letters like ä and © and £ and ç) also includes the letter eth, ð. I don't think it's used to denote any quantity yet. It wouldn't be the only non-Greek, non-basic-Latin letter used, either. For example, 1 Å = 0.1nm = 10-10m, and Å is in the same Unicode class (and general availability in typesetting) as ð.

9. No, it doesn't really need it's own symbol, I just wanted some symbol for convenience, especially for programming:

Code:
`const double phi = 1.059463094359;`
And also for use within text.

Unlike 2π (6.28...) for written equations and "twopi" for programming, "twelfth_root_of_two" is just a bit too long.

10. Couldn't you just call it a semitone ratio (21/12=ð or something similar in documentation/article, and semitone_ratio in code)? With a comment somewhere early on that it refers to the ratio of successive semitones in twelve-tone equal temperament (tuning), so that semitone_ratio = 21/12?

Begin rant:

To be honest, I've always had a bit of an issue finding proper labels for these kinds of things.

I don't mind symbols (Greek letters or otherwise), but what I really hate, is naming constants after their discoverer. I'm just not that interested in peoples' names; considering how every discovery is built on top of others' work, it's not like the discoverer's name should be revered. (And knowing quite a few profs, I think it's quite likely a lot of the discoveries were actually made first by their students or acquintances. There is, and always has been, quite a lot of competitive pressure, and a discovery popping out of vacuum is very, very rare..)

The history of the research and discoveries should be described in the background materials, not in the actual phenomena or constant. Math and physics are hard enough to remember without adding to the confusion with obscure historical details. (I'm not saying the history is irrelevant. It is important, and should not be overlooked, but idolizing persons by immortalizing their names in physical constants and laws just makes understanding the physics and mathematics described harder than necessary. Descriptive labels work better, is my claim.)

I find labels such as "Avogadro's number" (inverse mol) idiotic and more than a little idolizing, whereas something like "fine structure constant" is at least very descriptive.

End rant.

11. My programs tend to be math intensive, and I find them easier to read (and debug) if they resemble algebraic expressions, with simple variable names.

Certainly "semitone_ratio" works well as a name. The short names I like to use are simply a preference. Hence, a greek letter.

I wouln't propose that 2^1/12 should have it's own symbol. It happens to be very common in western musical scales, but aside from that, it has no special
mathematical significance. But as an interval ratio in general, a greek letter designation could make sense. For example, temperature expansion coefficients
normally use alpha. If you had a new coefficiiet of some type, alpha would be a logical choice. Since phi had already been put to use representing a ratio, I
thought it might as well represent another one also.