Perfect tuning

[Ian Rae]

The F# minor7 using the A and B pedals sounded at least as in tune as it does in ET but a whole lot sweeter.

Doesn't "sweeter" imply that it sounds more in tune?

The whole idea of ET is that everything is equally out of tune and you get used to it eventually. I am 65

[Steve Sycamore]

Doesn't "sweeter" imply that it sounds more in tune?

I think it's more than that. Some are satisfied to call chords in tune if there is no obvious beating. But beating only happens when the harmonics of 2 or more notes are close in frequency.

Sweeter, to me, means that the intervals are more clearly defined - vivid. The note's position in the chord or key is also more defined and vivid. The pitch of the note in a melody is in the exact right place to give it musical meaning - enough meaning to trigger musical and artistic imagination in the mind of a listener. Last but by no means least, each note, each interval, each chord and each key is unique and has its own identity. It wasn't cut from a factory "one size fits all" template as ET makes all notes.

[Steve Sycamore]

Here is the full breakdown for the E9 neck. The C# JI table is primarily for the A pedal/F lever combination, the F# table for the B plus C pedal combination and G# for the D lever. In the open position those produce a C# major, F# minor and G# minor chord, respectively.

In checking this I discovered that adding the D lever to the BC pedal combination gives an exquisite sounding augmented chord. The D lever drops the F# to an F at exactly the right pitch, at least on my Pro III and ZB Custom guitars.

[b0b]

In my opinion, specifying a tuning in cents beyond one decimal point is useless. Nobody can hear that. Most musicians can't hear differences of less than 2 cents anyway.

Here's my analysis of the E9th JI tuning: www.b0b.com/infoedu/just_e9.html

I no longer agree with the premise that just intonation is the best tuning for pedal steel. I've been using meantone temperament on my D6th for over 6 years now, and am quite pleased with it. My E9th is a simplistic temperament of my own invention, with A B and F sweetened by ear.

It would be interesting to set up two guitars at a show, one tuned JI and the other meantone, and see how many people could tell which was which. Meantone has the advantage that you don't have the "two F#'s" problem to deal with. Other than that, I'd be hard pressed to hear a difference.

[Ian Rae]

What's the opposite of a eureka moment? I don't know the Greek for "Duhh!"

The title of this thread is "Perfect Tuning" and having had a scientific education, I took it mathematically. I now realise that Steve's perfection is of an altogether more poetic and elusive kind, not so much a perfect triad as a perfect steak.

Although I think of my tuning as JI, in practice it is very slightly stretched (b0bified?) for safety, and I'm beginning to wonder if it isn't the natural intervals but the tiny amount of stretching that makes it sound good!

[Steve Sycamore]

In my opinion, specifying a tuning in cents beyond one decimal point is useless.

I agree, from the perspective of a "one off" measurement. But, if you have any in-depth experience with mathematics than perhaps you begin to understand how rapidly even slight errors rapidly multiply into significant and audible artifacts as you start applying algorithms and tools to do more sophisticated calculations. That has to do with "round off" error. But also, as I have said, some people are *extremely* sensitive to pitch offsets in melodies.

Thanks for the very valuable page on Mean Tone Temperament. Certainly 4ths and 5ths are much less sensitive to precise pitch deviations - both harmonically and melodically. And that makes them probably an ideal place to absorb offsets that disturb a continuous application of the most desired major and minor third intervals. It seems we have come a long ways in understanding the technology involved with our music. But there is still more to learn, understand and adapt to.

[Brint Hannay]

What is the "two F#'s" problem? I've seen it referred to before, but I don't understand what is meant by it.

I personally don't have any problems with F#'s. I tune my E9 to meantone temperament. Both the 1st and 7th strings are tuned the same, and in both octaves they function, to my ear, equally well as fifth of B, root of F#, third of D, and seventh of G#. These intervals fall between the ET and JI values. No difference between the octaves, and all functions work well.

But then, I am not one who feels that only beatless intervals sound good, i.e. "in tune".

[Ken Metcalf]

Try comparing the 5th string and 1st string then compare the 5th string with A pedal to 1st string.
Check what happens to your 6th string with A&F

[Ian Rae]

Brint, if you tune all the other notes of the E scale in natural intervals and leave F# to last, you discover that it can be a perfect 4th below B to use in a B chord, or a perfect fifth below C# to use in an F#m, but it can't be both. In the former case it's 9:8 above E, and in the latter it's 10:9. (The ear recognises both these intervals as a whole tone.)

To me the B chord is more important and there are plenty of other minors that are in tune.

[Brint Hannay]

In the 2.5 meantone that I use, F# is tuned to 0, B is tuned to +2.5, and C# is tuned to -2.5.

This results in the B->F# fifth and the F#->C# fifth both being -2.5 cents relative to ET--their inversions, the fourths, of course therefore being +2.5. These deviations are small enough to be acceptable to my ear, and thus I find no problem with tuning the F#'s.

(D is tuned to +10, making the D->F# major third -10 (like all the other major thirds) 3.7 cents sharp of JI. This, too I find not only acceptable but pleasing to my ear.)

YMMV.

[b0b]

What is the "two F#'s" problem? I've seen it referred to before, but I don't understand what is meant by it.

I personally don't have any problems with F#'s. I tune my E9 to meantone temperament.

My point exactly. In meantone centered on the 9th (F#), the problem moves to the #5/b6 tone, which is out of the diatonic scale and not even a standard pedal on E9th (the C note). In meantone, the F# is nicely in tune with the B, C#, D and D# notes. No problem.

[Ian Rae]

Although I don't feel as though it would solve any problem for me, I really ought to be able to get my head round the theory of meantone. I have a smartphone app with a load of different versions of it.

I failed last time I tried to understand it - where can I find a good explanation?

[Ken Metcalf]

Google Mean tone tuning

https://en.wikipedia.org/wiki/Meantone_temperament

https://www.youtube.com/watch?v=SWLpPF4f1XA

[Charlie McDonald]

Meantone is an equal temperament as well; meantone 6 has a slightly rougher curve than meantone 12 comma.
It probably lacks the mathematical beauty of a perfect tuning,
but I think fault-tolerant is more important in pedal steel which has a slidey scale to begin with.

Certainly 4ths and 5ths are much less sensitive to precise pitch deviations - both harmonically and melodically. And that makes them probably an ideal place to absorb offsets that disturb a continuous application of the most desired major and minor third intervals.

To me, 'discovering' meantone 6 (I think, using increments of 2.5 cents) meant not having to get my head around a system.
I have yet to learn to tune it by ear, but I'm not really interested and tuners are available. For some reason, yes, F#'s were no longer a problem.

If someone set up a comparison as b0b suggested, I think that he and I both would have to be told that it is for the purpose of tuning comparison
before we would begin to hear which is which, and the answer would probably be a 50/50 guess, regardless whether one or two players were used.

[Steve Sycamore]

But I think you need to consider not just the experience of the listener, but also the player. The player may or may not experience a "kick" from a particular tuning. I would guess that the greater amount of energy and inspiration a player gets will translate to something that the listener can feel and appreciate.

I did a very quick analysis of 3 tuning systems. For the E9 neck they look like this:


For some reason the Quarter Comma Mean Tone seems to break up heavily when applied directly to E9 playing options.

[Alan Bidmade]

I was hoping Jack Stoner might have chipped in here. I don't quite know how I would apply the various tunings as given in this thread - but, Jack's tuning (which he kindly makes available via Peterson Connect if you contact him) is the best yet. My Ben-Rom always sounded pretty good with the Emmons sweetener, but Jack's tuning (based on Jeff Newman's tuning) has my Ben-Rom sounding fantastic!
Highly recommended.

[b0b]

Not quite enough information was available from Bob's C6 chart to translate and fill in all of the Mean Tone values. For some reason the Quarter Comma Mean Tone seems to break up heavily when applied directly to E9 playing options.

Here are my C6th meantone numbers adapted to the E9th, where F# is the center point:

C +15
G +12.5
D +10
A +7.5
E +5
B +2.5
F# 0
C# -2.5
G# -5
D# -7.5
A# -10
E#(F) -12.5
B#(C) -15

[Brint Hannay]

Steve, I was wondering where you got your figure in your Mean Tone chart for minor third in "A tonality". As b0b's chart above showed, in F#-centered sixth-comma meantone the C note, depending which way one cycles around the circle of fifths, would be either at +15 or -15, and thus the minor third interval from the A root (+7.5) to C would be either +7.5 or +22.5 (!).

Given that my guess is that probably the most used application of a C note in E9 (achieved in most cases by a "split" between the A-pedal C# raise and an A# lower) would indeed be as the minor third of A , tuning that C to +15 would be the clear choice, as the resulting minor third interval A->C would be +7.5, consistent with the other minor thirds in your Mean Tone chart.

[b0b]

Right, Brint. The A+X pedal split is typically tuned for the Am chord (pedals A+X+B), which would use C+15. If you were tuning it for a C#Maj7 (pedals A+X+F), you would tune it to the B#-15.

That's the problem with meantone - b6 and #5 are two different notes. It's C vs B# on E9th, Ab vs G# on C6th.

But that's an advantage over JI, where the problem of two F# notes has to be dealt with in most of the common E9th major scale positions.

I've always suspected that the A-Ab lever on C6th was the real reason that Buddy Emmons switched to equal temperament. There's no other way to tune it that will work with all of the jazz chord possibilities.

[Steve Sycamore]

I've updated the chart with Bob's E9 figures. They come out right on the money.

That's eye opening about Buddy Emmon's use of ET. I always felt there was something very different about his sound and note choices. That must be the reason.

[Stefan Robertson]

Had a play with some of these tuning pitches and on my short scale Lap Steel Guitar some notes sound way out to my ears.

My tuning has All the E9 stings except my C# instead of a D# giving me a 13th for non - pedal.

What would you guys recommend if you were tuning for a short scale Lap Steel Guitar E9.

I got interested in the idea of my Peterson by default uses C instead of E so how would I go about calculating this?

[Steve Sycamore]

For an E9 or E13 guitar without pedals you would want to tune F# to +5.9 if you use JI with the chart I provided. I checked the Peterson tuner and it uses A based JI rather than C.

I updated the chart a few posts above because I used the wrong F# in calculating the 5th tone of the F#m chord. In that situation you play the F# that is raised in pitch by the pedal.