Your Tuner is Lying
The E is a lie.
That’s not E. It’s close, but everything is relative.
All will be revealed.
I was doing some research today for one of my students who is working on intonation and I collected this information on Just Intonation. I have compiled it into a table for easy reading.
| Chromatic Scale Degree | Equal Temperament | Just Intonation | Deviation from Equal Temperament |
|---|---|---|---|
| 1 | 0 cents | 0 cents | 0 cents |
| 2 | 100 cents | 88 cents | -12 cents |
| 3 | 200 cents | 204 cents | 4 cents |
| 4 | 300 cents | 316 cents | 16 cents |
| 5 | 400 cents | 386 cents | -14 cents |
| 6 | 500 cents | 498 cents | -2 cents |
| 7 | 600 cents | 600 cents | 0 cents |
| 8 | 700 cents | 702 cents | 2 cents |
| 9 | 800 cents | 814 cents | 14 cents |
| 10 | 900 cents | 884 cents | -16 cents |
| 11 | 1000 cents | 971 cents | -29 cents |
| 12 | 1100 cents | 1088 cents | -12 cents |
OK. So what?
This information, more than any other, is crucial for playing in tune. For years I have been taught about my instrument’s tendencies (A is sharp, B is flat, etc.) and even taught how to adjust. It wasn’t until I started playing with a quartet and really working on intonation that I began to understand how intonation actually works.
From the chart we can see that scale degree 5 (the tonic major third) is WAY too sharp in the Equal Temperament system. Don’t even get me started about the dominant 7th of the tonic major triad. (Seems like the Equal Tempered guys never thought of modulating to the sub-dominant, but I digress). Somewhere along the way we tricked ourselves into being cool with out of tune-ness. It’s way easier to just accept being out of tune that to actually tune things. (If you agree with the last statement, stop right there cowboy. Your work is done.)
I can site probably 20 recordings of saxophonists who were taught the same way I was, and it shows. Every pitch that I was told was heinously sharp is heinously flattened without a thought regarding where the pitch was supposed to be. I even came across a discussion forum where some one was advocating that flat notes = dark sounds and sharp notes = bright sounds. It astounds me that this still goes on. Our country has enough problems already so let’s just end that debate right here. Flat = flat ; sharp = sharp. Full stop. If you want a dark sound you need to find a different way than playing out of tune. Sorry, Charley.
So there’s the chart. Learn it. Want one to print out? Take mine. Want just a few bullet points to remember? OK, fine:
- Major thirds and minor sixths are 14 cents sharp on your tuner. To play them in tune you must lower the third 14 cents. 14 cents is a lot, so it’s time to limber up the golden pipes and get flexible.
- Perfect fifths and fourths are only 2 cents out of tune on your tuner. That is undetectable to most people, so don’t sweat it. You’re cool.
- The major sixth/minor third is super flat. If you are a reed player and you have the third in a minor chord you will probably need to resort to an uncomfortable amount of biting. Violins have it so easy.
- The octave and the tritone are the only perfect intervals in both equal temperament and just intonation. Only one of these will be really useful though. I’ll let you guess which one.
- The leading tone of a dominant chord is a lot sharper than your tuner says. Half steps are only 88 cents apart. If you try to tune the minor third between the seventh and the fifth of the chord you might just get there. The tritone between the seventh and the third is a lie.
Final point: knowing your instrument’s pitch tendencies is very important, don’t get me wrong. But the guessing game we call tuning gets a whole lot easier when you understand your tuner’s pitch tendencies first.