# Technical Question about Hz and the changing distance between notes

Discussion in 'Miscellaneous [BG]' started by Lokire, Apr 20, 2006.

1. ### Lokire

Aug 21, 2003
Seattle, Washington

We were talking about singers and how it's usually harder for women to control their pitch when they sing down low. My friend rationalized that it was because in the lower pitch range, there aren't as many hz inbetween each note, so you have to be more precise. There isn't as much room for error - and that was the reason why. (Leaving out the natural range of gender specific vocal cords for the purpose of the argument)

If you think about it in terms of Hz = pitch: Take one note, say an A and then go an octave above that to the next A. The hz value should be double, correct? If A=440, then the next A would be 880, right? That's a difference of 440 hz.

Now take a lower note, with a frequency of 120hz. Double that to get an octave higher and you have 240hz. That's a difference of 120hz.

So in terms of hz there is a greater distance between higher notes than lower notes. But when I think of it in terms of basses (I'm a bassist, my friend is a sound engineer ) I know that there's a greater distance between the lower frets of a bass whereas the higher frets are spaced closer together. Like on a fretless bass, it's much harder to intonate up higher on the fretboard because a little difference in position can be a whole other note, where down lower on the fretboard if you're a little bit off it's still pretty close.

So I'm confused. Does that value of 1hz change as you add them together, or am I missing something else here?

2. ### Richard Lindsey

Mar 25, 2000
SF Bay Area
Don't be offended, but I think your entire premise is wrong. I'm not intimately familiar with the physiology of pitch production, so don't take this as The Word From On High, but just from the standpoint of superficial plausibility and logic, I doubt that the difficulty of singing in pitch has anyhing to do with the lower number of cycles per second. You seem to be thinking that if you miss the "correct" Hz, you automatically have to go to the next. Like, if you miss 100 you have to go to 99 or 101. But you don't. There's no reason why someone can't emit a pitch of 99.9 Hz.

I suspect the real issue is that the notes are simply approaching, or exceeding, the limits of the singer's range. Singers generally do better with notes within their range; you might say that that largely determines what their range in fact is. Men don't do well with low notes either when the notes are outside their range. And both genders have problems with notes above their range as well.

3. ### Richard Lindsey

Mar 25, 2000
SF Bay Area
Apples and oranges, my friend.

Incidentally, although the frets do get smaller as you go up the neck, there is a sense in which the *relative* size of the fret does not change at all (leaving aside the small intonation factors imposed by string type etc). For example, the distance between the the nut and the 1st fret is a given fraction of the distance between the nut and the bridge. However, the distance between the 1st fret and the 2nd is *the same fraction* of the distance between the 1st fret and the bridge. And the distance between the 2nd fret and the 3rd is *the same fraction* of the distance between the 2nd fret and the bridge. This is why capos work, regardless of whether you downtune the open strings or not.

4. ### Lokire

Aug 21, 2003
Seattle, Washington
No offense taken, I'm just trying to sort this out (to myself) and get another viewpoint

Actually, I agree that the whole premise is wrong, and I agree with your view. In my opinion it has everything to do with a person's range and their skill, rather than Hz or anything technical like that. That was just the initial idea that got me starting to think about the distance between notes and Hz.

I wasn't trying to say (or imply) that there wasn't anything inbetween Hz values either. I was just keeping to whole number for simplicity sake.

I see what you're saying about the fret/bridge ratios being equal and that makes sense. I hadn't been thinking of it that way. Thanks!

5. ### Petebass

Dec 22, 2002
QLD Australia
Lokire, I must say I admire those who can not only think in an abstract way, but aren't affraid to speak up about it and ask questions. I wish I was more like that sometimes.......

6. ### SuperDuck

Sep 26, 2000
Wisconsin
Just as an addition to this thread - keep in mind that the term "pitch" is purely subjective one. Perceived pitch can change with the amplitude of whatever sound your listening to. It's the human recognition of how "high" or "low" a sound is. Frequency content, however, is a purely objective quantity that can be measured.

7. ### Bob Lee (QSC)In case you missed it, I work for QSC Audio!Commercial User

Jul 3, 2001
Costa Mesa, Calif.
Technical Communications Developer, QSC Audio
In the even-tempered scale that Western music (not to be confused with country and western) uses, the interval between each note of the chromatic scale is 1.05946, or 2 to the 1/12 power. Using this frequency ratio, if you ascend 12 chromatic steps, you end up on the same note you started on, but one octave higher (2× frequency).

It doesn't matter that the "Hertz" are closer together among the lower notes; the ratio of the frequencies is still the same whether you're in the deep bass octaves or in the very high registers. It has nothing to do with vocal pitch control.

8. ### Cloggy

Apr 5, 2006
The 12th root of 2 (or its reciprocal) is also the amount by which the frets distance apart increase/decrease.
A fret spacing of 2" multiplied by 0,94387431268169349664191315666753 12 times would give a fret space of 1".All the values in between are proportionally correct.
Going the opposite direction it's × 1,0594630943592952645618252949463

9. ### Cloggy

Apr 5, 2006
BTW,1Hz to 2Hz is an octave too.
3Hz is an octave and a fifth,5 Hz is 2 octaves and a major third,7Hz is the minor seventh above,9Hz is a tone .
Untempered.
The proportions remain the same whether there a loads of cycles between them or very few.
It's a numbers game.

10. ### WillPlay4FoodNow With More Metal!Supporting Member

Apr 9, 2002
Orbiting HQ
Which plays directly into the original question and I would wonder the same thing too. A low B I believe is 31Hz while the A one step below is 27.5Hz (440/2 = 220/2 = 110/2 = 55/2 = 27.5). This leaves little wiggle room if your vocal chords aren't nailing 31Hz.

A few octaves up and you're talking about hundreds or thousands of hertz between each scale tone.

I know I saw a paper somewhere which tied the space between the notes to the Golden Ratio. The Golden Ratio of course seems to be the real answer to Life, the Universe and Everything (just kidding, but between that, pi and e you get lots of connections from very un-round numbers).

11. ### Bob Lee (QSC)In case you missed it, I work for QSC Audio!Commercial User

Jul 3, 2001
Costa Mesa, Calif.
Technical Communications Developer, QSC Audio
It's the same narrow wiggle room anywhere, whether it's low notes or highs.

12. ### SuperDuck

Sep 26, 2000
Wisconsin
Yeah, it's pretty amazing when you see it applied to life around us. I would recommend that anyone who enjoys a scientific viewpoint to check out a book or two on the golden ratio from their local library.

13. ### Richard Lindsey

Mar 25, 2000
SF Bay Area
Again, this just doesn't matter at all. The distance between A and Bb is always relatively the same. Missing a 31 Hz B by 5% doesn't make you any more out of tune than missing a 62 Hz B by 5%. The fallacy is that thinking Hz is a measure of distance. It's not.

14. ### Bob Lee (QSC)In case you missed it, I work for QSC Audio!Commercial User

Jul 3, 2001
Costa Mesa, Calif.
Technical Communications Developer, QSC Audio
To show you how irrelevent "the number of Hertz" is between notes except as ratios of the pitch frequencies, you can invert the relationships and look at wavelengths.

At 20º C, the wavelength of your low B (30.87 Hz) is 10502 mm, and a low C (32.70 Hz) is 11124 mm. With these two notes, that 1.83 Hz difference is also a wavelength difference of 9622 mmover 30 feet different!

Now look at the same two notes in the octave above middle (440) A. B is 987.77 Hz, for a wavelength of 348 mm, and C is 1046.5 Hz, for a wavelength of 328 mm. Now the difference between the two frequencies is up to 58.7 Hz, but the difference in wavelengths is only 20 mmless than an inch.

So which are closer together, the low notes or the high ones? Answer: neither. What matters is the ratio between them. As Cloggy mentioned, 1 Hz and 2 Hz are an octave apart. So are 1000 Hz and 2000 Hz. Octaves are always a relationship of doubling the frequency and halving the wavelength, or halving the frequency and doubling the wavelength. All the 11 chromatic notes in between are just equally spaced along those exponential relationships.

15. ### Cloggy

Apr 5, 2006
Indeed
All new notes start on uneven new numbers,since all even numbers are multiples of a lower uneven .
One 'wave' kicked into a higher vibrational mode gives a higher tone:
1 is the root(+2,4,8 etc)
3 is the fifth (+6.12.24 etc)
5 is the third (+10,20,40 etc)
7 is the minor 7th
9 =9th
11 = nearly 4th
13 = 6th
15 =maj 7th