It Hertz to Have No Cents
I am in the process of reading through about 60 pages of feedback, ideas, and questions on harmonica technology and music- notes copied and pasted from your emails into a word document. Thank you for this overload to my questionnaire! While I was studying these notes I came across some questions about tuning that reminded me of a note that i made many years ago in my my beat up, dog -eared, highlighted copy of Steve Baker’s Harp Handbook.
The note was this: “4 cents = 1 Hz”
I Wrote this note down many years ago when this fact was given to me by a well known harmonica expert who shall remain nameless. I wrote this down like it was some sort of gospel that explained one of the mysteries of life. At the time I was grateful for this knowledge, and figured it would come in handy some day. I am not sure how long I believed this piece of information, but last night it surfaced in my mind again along with the understanding that it is total nonsense.
Now I am not the sharpest tool in the shed when it comes to math, so it does not take long to confuse me when you start using numbers to talk about tuning musical instruments.
So if you find yourself wondering what is up with Hertz and cents, I feel your pain and I want to do something about it right now.
Here is the deal: you can’t translate Herttz into cents the way you can convert inches and feet into meters, or dollars into euros.
It doesn’t work that way.
Hertz are cycles per second, or rate of vibration. The more hertz, the higher the pitch. You measure hertz by counting the number of cycles per second. Hertz are used in tuners to calibrate your tuner (set the standard that you use for tuning).
A 440 refers to one tuning standard. The A note in this standard vibrates at 440 cycles per second. All of the rest of the notes in this system will be tuned in relation to this note. When you increase this reference note to A 442, then all the other notes will go up in relation to this higher rate of cycles per second.
You tune harmonicas sharper to make them sound in tune with other instruments, so you need to know how to calibrate your tuner, and many tuners show the tuning standard as A 440 Hz as a starting point. Hz is the short way to say Hertz.
BTW, Hertz are named after Rudolf Heinrich Hertz (1857 – 94) a German physicist and pioneer in radio communication. He was the first man to broadcast and receive radio waves, and I am personally grateful to him for making it possible for me to listen to Stevie Wonder when I was a kid with an earplug in my ear and a battery radio in my pocket.
Once you calibrate your tuner by raising the A 440 Hz to 442 Hz ( or higher) for all practical purposes you are done with Hertz for the rest of your tuning adventures.
From that point on, you will be looking at a needle or lights that tell you something about cents.
Cents show you how close you are to the note you are tuning to, but not by simply counting the cycles per second.
The easiest way I can think of to understand how cents work is to compare cents to percentages. Five percent (5%) of $100 is $5. Five percent (5%) of $1000 is $50.
Same percentage, different number of dollars.
The same basic thing happens with cents on a tuner. As you go up the tuner in octaves, you keep doubling the number of cycles per second. If you used Hertz to keep track of how flat or sharp you wanted a note to be, you would need to keep doubling any variation of flatness or sharpness. as you tuned notes in the next octave up. You would need new numbers for each octave for each note. A 110 Hz, A 220 Hz, A 440 Hz, 880 Hz, etc. And those are the easy numbers to keep track of……
Now is a good time to take a deep breath……
The good news is that you don’t have to do that because your little tuner does two things: it measures the vibrations per second, and then translates the measurements into a percentage (how many cents) sharp or flat your note is, no matter what octave it is in.
Then it shows you this “percentage” with a needle or lights so you don’t even have to count cents if you don’t feel like it.
ONe last thing -the word cents is derived from the word for 100. There are one hundred cents between one musical note and the next half step up. In other words 100 cents equal 100% of the way from one musical note to the next half step note.
That is, if you want all your notes evenly spaced apart, and not everybody does. THAT is another can of worms for another day….)
I sincerely hope that is has been at least a little entertaining. If you already understand this, why didn’t you tell me this 25 years ago?
This kind of thinking only Hertz for a little while until it makes cents. Sorry – just can’t help myself…..