Equal Tempered Tuning

[Ian Rae]

Ian, the values were not calculated, they were observed.

That's certainly what I meant to convey - finding by practical means tuner settings which would give a pleasing result. It's me that's just done the calculating and had my eyes opened.

[Ian Rae]

In case anyone's interested, here is the crucial part of the Emmons chart with its real pitches.



The A/B & A/F triads are natural to the accuracy we have, and the open E is close despite its even-tempered 5th. The B chord on 5, 2 & 1 is natural but string 7 is a compromise. It's slightly flat for the B chord rooted on 10 but still sharp for the F#m on 7 - maybe that's intended to exploit cabinet drop.

[Jim Reynolds]

I guess then, bOb, I'm an idiot. I think that most of my musical life, everything was mostly measured in hertz. Sorry for my ignorance.

[Ian Rae]

I think b0b is acknowledging the establishment view that a hundredth-of-a-semitone unit takes care of any likely microtonal organisation of the musical scale.

I had a scientific as well as a musical education and I prefer to think in Hertz, using as many decimal places as I please.

[b0b]

Thinking or showing your tuning in Hz is one thing. Saying that "I tune E's to 440 Hz" is just wrong. The frequencies around 440 Hz are all A notes.

Ian's chart shows the actual Hz frequencies. Unless you have a tuner that displays them, those numbers aren't very useful. Almost all musical tuners made today show the cents scale, or they have no numeric reading at all.

[Jim Reynolds]

I don't think I ever said "I tune my E's to 440. I said that None of my string on my steel are tuned to 440. They are all either sharp or flat of 440. Again, let's just play. if it sounds good play. When I started NO one know what or where to tune to.

[Ian Rae]

Unless you have a tuner that displays them, those numbers aren't very useful.

I do, but he's right! - they aren't once you've realised they represent natural intervals.

I was dismissive of the deviation charts at first, but I realise now that they are a foolproof method of getting a sweet tuning if you're not sure what you're listening for or you plain can't hear.

[b0b]

I don't think I ever said "I tune my E's to 440. I said that None of my string on my steel are tuned to 440. They are all either sharp or flat of 440.

It's a pretty safe bet that all of your strings save one are flat of 440 Hz. The third string with pedal down is the only one that's close to 440 Hz. Everything else is well below that.

[Jim Reynolds]

Most are tuned above 440. F#'s 441.5 G-444.5 D#'s-439, D-439/C#-438. G#-439, A's 441 , E's-442.5 C Pedal F#-439.5 D# Lever-440.5, F Lever 435.5 B's-442, A Pedal C# 438.5, C Pedal C# 438.5 6. G#-439 B Pedal A441, D on 9th 441.5 , D439
This my set up. It is tuned to Hertz. As you can see, without counting, they are about tic for tac. It does sound good to me, and it is right from Jeff Newman Tuning Chart. I also used his tuning in the 80's when he was set the E's at 440 and lowering the D lever to 438.5. There were other change differences too, but I don't remember them. I do have the old tuning chart is interested in seeing it. On this there are 7 string tuned above 440, that would leave 3 tuned below. The pedals and levers you'd have to count. Hope everyone had a Very Merry Christmas, and I really enjoy all of you. God Bless and hope for a full a joyous New Year.

[Ian Rae]

I think we need to accept that two languages are being spoken here.

b0b means that the high A on string 3 will be around 440Hz, but the E on string 4 will be in the region of 330Hz, and so on down to the 10th-string B which will be around 125Hz.

A person who says "I tune my Es to 442" means "I tell my tuner the white lie that I want my As to be 442Hz and then I tune my Es to what it tells me. I don't know what that is in Hertz and I don't need to."

Many people speak this language for historical reasons to do with tuner design. I happen to belong to the Hertz-speaking minority but I can get by in it.

[Jim Reynolds]

I speak in Hertz too, but you sure lost me, or you have no idea what I just put on here. I know I will drop this right now, and I guess I should have, but I was only trying to make it simple for a new player. Sorry for all the higher educated people.

[Ian Rae]

I think the best this has ever been explained, was by Jeff Newman. It is very easy for the average person to understand ...... As said before it is a touchy subject, but as long as it sounds good, JUST PLAY.

Your advice is good, Jim. My tinkering with numbers has shown me that I've been tuning the Newman way since I started but without realising, as I came there by a different route. It does sound good and anyone can use it.

[Jim Reynolds]

Ian, thanks, and keep the good ole country music alive over there. Sorry it died here. Have a good one.

[Charlie McDonald]

If you want to talk about temperaments with other musicians who don't play pedal steel, use should use cents. Otherwise you sound like an idiot.

I believe b0b is using the impersonal 'you,' a conditional case meaning 'anybody.'

If you need to translate one of those old Hz charts, think of it as 1 Hz = 4 cents. So instead of saying "I tune my E's to 442 Hz", say "I tune my E's 8 cents sharp". Then you can argue about it intelligently.

I'm not sure we can argue intelligently.
None of our equal temperaments seem equal.

I guess then, bOb, I'm an idiot. I think that most of my musical life, everything was mostly measured in hertz. Sorry for my ignorance.

Let me help you feel better.

I stumbled onto this post in the 'Ask Buddy' archive, answering the question whether Mr. Emmons tunes straight up to A=440:

From: Buddy
Date: 26 Feb 2002
Yes. I tune the thirds to around 438 or 439....

I could say that makes no sense, but we realize he's trying to communicate something simply in Hz deviation.
He means he tunes his thirds narrow by 4-8 cents. It would seem that some terminologies should be changed.
Hertz make no sense to cents people; cents just hurts Hz folks; it may take a while for the dialogue to evolve.

[Earnest Bovine]

Most are tuned above 440. F#'s 441.5 G-444.5 D#'s-439, D-439/C#-438. G#-439, A's 441 , E's-442.5 C Pedal F#-439.5 D# Lever-440.5, F Lever 435.5 B's-442, A Pedal C# 438.5, C Pedal C# 438.5 6. G#-439 B Pedal A441, D on 9th 441.5 , D439
This my set up. It is tuned to Hertz.

<facepalm>

[Alan Brookes]

We've drifted off-topic. The topic was about Equal Temperament, which is about the relationship between notes, not the pitch tuned to. Not every orchestra in the world tunes to the same pitch, and in previous centuries the pitches were lower than they are nowadays.

But the principles of Natural Temperament, Equal Temperament, etc., apply no matter what primary pitch you may be tuning to.

In fact all the rules of harmonics still apply outside of the hearing range of human beings, so other creatures can probably hear chords and dischords above and below our hearing threshholds, which to use are completely silent.

[Ian Rae]

A couple of pages in is always a good time to look back at the original question.

I have read and "understand" why some players use tempered tuning.

So that's good. Just a guy celebrating his intellectual advancement - no question, and no need for any replies. But if I'd paid better attention I wouldn't have learnt as much as I have. I even know what a cent is now

[Jim Reynolds]

Yes, Ian, I love Charlie's statement of a Hertz, and a cents. I learnt something's too. Have a great year.

[Jim Reynolds]

I , too, thought it was about tempered tuning, but I have been wrong many times. Like you I guess we need to go back and check the original, thanks for doing that.

[Jim Reynolds]

Alan, if you'll look back to see what you wrote about Bach, you'll see it was the same as I was saying. Except I don't think keyboards ever had strings in Bach day. Not sure, but you do know a lot about music. Most young people today don't even know who Bach was. Have a great year. Look forward to more from you. Thanks

[b0b]

Bach did not invent equal temperament.

Harpsichords have strings.

Young musicians today still study Bach.

Hz is a measurement of frequency in cycles per second. If two strings are both tuned to 440 Hz, they will both produce the same note (A).

I give up.

[Jim Reynolds]

bOb, I think would find fault with anything. I never mention musicians, I said, young PEOPLE. Big difference. Your right though, I'm out of here.

[Charlie McDonald]

Me too, but I'm entirely grateful, Bob, for the link to equal temperament and the new Wikipedia.
If I'm smart, it should keep me busy for a few years.

[Steve Mueller]

I've been using a Peterson 400 strobe tuner I bought in the early 70's. It's an enlightening perspective on tuning. You can tune the all 10 strings and most of the pedals on the E or C neck on the E or C note setting respectively only using harmonics. The just intonation 2nds, 3rds, 4ths, 5ths, 6ths and major 7ths all show up when you strike the harmonic at the 5th, 7th or 12th fret. You can adjust the number of cents variation from equal temper for each one according to your personal taste. I found the longer I play the flatter the 3rds sound when they're tempered. One thread I read by Emmons stated that he tunes everything to 440 open(except 3rds if temperature could cause them to snap)and then tunes the pedals with harmonics to account for any mechanical variations(cabinet drop/raise). I think this makes the most sense of any explantion I've read. With the Peterson 400 you can see the exact amount of cabinet drop/raise for each pedal change and then tune visually using the harmonics. Using this system my current temperments have all open stings and nearly all pedal changes within 2 cents of equal temper on both necks. If you had a steel with zero cabinet drop/raise, to my ear I think you could tune everything to ET. I've been able to play more freely without as much worry about variations from string to string.

[Charlie McDonald]

Yes. I tune the thirds to around 438 or 439....

He said he began doing so in studios where the a/c was too much, presumably from the sharpening effect of cold strings, I'm guessing.