C6 Mean Tone Temperment

Scott Swartz · Post by **Scott Swartz** » 19 Mar 2003 8:51 am

Nothing gets a day going like a good tuning discussion, so here goes.

I received an email regarding programming a Peterson 490 Strobe Tuner for C6, and I use a mean tone approach on C6 that I thought I would post for discussion. There have been discussions of meantone on SGF before but here is a detailed look at it. Its basically a concept that narrows the 5ths by about 3.6 cents around the circle of 5ths, which makes the thirds just temperment in most keys.

I start with D=0 cents offset in the circle of 5ths. Then everything is raised 5 cents ala the Newman charts to make the zero fret more "in tune".

Here are meantone offsets that I use for a C6 tuning. Note that certain triads are not in tune in meantone, specifically the major keys of F#, B, C#, E.

Note Offset (cents)

G# +25.7
D# +22.6
A# +18.6
F +15.4
C +12.0
G +8.6
D +5.0
A +1.7
E -1.4
B -4.7
F# -8.3
C# -12.0

Here are some triad interval example using the above at fret zero.

<pre>
C Major Chord
G---------------------------|
697 cents
E------ |
| 386 cents |
C----------------------------

F Major Chord
C---------------------------|
697 cents
A----- |
| 386 cents |
F----------------------------

G Major Chord
D---------------------------|
697 cents
B----- |
| 386 cents |
G----------------------------

A Major Chord
E---------------------------|
697 cents
C#----- |
| 386 cents |
A----------------------------

D Major Chord
A---------------------------|
697 cents
F#----- |
| 386 cents |
D----------------------------

A Minor Chord
E---------------------------|
697 cents
C----- |
| 311 cents |
A----------------------------

D Minor Chord
A---------------------------|
697 cents
F----- |
| 310 cents |
D----------------------------

E Minor Chord
B---------------------------|
697 cents
G----- |
| 310 cents |
E----------------------------

C Minor Chord
G---------------------------|
697 cents
Eb----- |
| 311 cents |
C----------------------------

</pre>

As discussed above mean tone falls apart for triads in the major keys of F#, B, C#, E. Here are some that will therefore be out of tune at zero fret.

<pre>

E Major Chord
B---------------------------|
697 cents
G#----- |
| 426 cents |
E----------------------------

B Major Chord
B---------------------------|
697 cents
G#----- |
| 426 cents |
E----------------------------

</pre>

If you want an approach to try other than the normal JT (ala the Newman chart) or tuning straight up, its worth a try.

[This message was edited by Scott Swartz on 19 March 2003 at 08:55 AM.]

Earnest Bovine · Post by **Earnest Bovine** » 19 Mar 2003 9:04 am

Its basically a concept that narrows the 5ths by about 3.6 cents around the circle of 5ths, which makes the thirds just temperment in most keys.

I like this approach and have used it for many years on E9 and C6. Actually I find 3.6 cents is too much; the thirds are too pure for playing with other musicians, and I use about 2 or 2.5 cents. This results in major thirds that are 8 to 10 cents narrower than ET, which sounds good with other players, and leaves a safety margin in both directions when the strings and pedals are not perectly in tune.
This gives 7 good sounding major triads (at each fret); i.e. 3 steps around the circle of 5ths in each direction. So on E9 these major triads (and their relative minors) sound good: G,D,A,E,B,F#,C#. The others are not usable, and require moving the bar to another fret.
And open strings on C6 allow good sounding major triads on Eb,Bb,F,C,G,D,A.

C Dixon · Post by **C Dixon** » 19 Mar 2003 9:11 am

Thank you for posting that. And I understood and am with you all the way.

I have struggled with C6 and now B6 on my U-12 for years. Following pretty much with what you are saying.

The problem is a simply one for me. I must have the major and minor thirds pure JI (except in a few cases). This is because I play C6 like JB does; only I add a lot of voicings using the lower notes which C6 permits.

Because of this anamoly, I have found NO way that satifies me better than to tune the following way:

Open strings; straight JI with strings 3, 7 and 9 at 440 reference.

Pedals 4, 7 and 8 and the knee lever lowering 3 from C to B, I tune straight JI.

Pedal 5; 1st string JI, strings 5 and 9 ET. Finally string 10 JI.

Pedal 6; 2nd string JI and string 6 ET.

Knee lever raising 4 to Bb is ET.

Knee lever lowering 4 to Ab is JI

Knee lever raising 3 and 7 to C# is JI.

So meantone would not get it for me, NOR would Straight ET or straight JI. But I can see how it might be great for those that play C6 the way BE, PF or most others play it.

So try it, ya might like it,

May Our precious Lord bless you in your quests,

carl

chas smith · Post by **chas smith** » 19 Mar 2003 9:40 am

Were you to tune a piano in mean tone, and you started the cycle on C, C->G->D->A->E->B->F#->C#->G#->D#->A#-(E#) F->C, the C's will be out of tune by 81/80, this is called the Comma of Didymus. When I was in high school, I tuned my mother's piano to mean tone and she wasn't too happy about it.[This message was edited by chas smith on 19 March 2003 at 09:41 AM.]

Bobby Lee · Post by **Bobby Lee** » 19 Mar 2003 9:47 am

I used meantone temperament on my F Diatonic tuning, and found it very pleasing to the ear. I used a 3 cent comma, so the thirds weren't perfect JI but they were pretty close. Here are some tracks made with it:
http://soundhost.net/b0b/radio/Courtship.b0b.mp3
http://soundhost.net/b0b/radio/Waltz_in_C.b0b.mp3

The biggest advantage to meantone, in my opinion, is that you don't have to compensate that pesky 9th tone. The thirds sound a lot prettier than ET, too.

I found it to be sort of harsh on jazz chords, though. I ran into a few places where a combination of notes was unusable because they were on opposite sides of the circle. Diminished 7th chords in particular didn't pan out too well. That might have been more a side effect of the copedent than meantone. I understand that Earnest has no problem with jazz chords.

------------------
<img align=right src="http://b0b.com/b0b.gif" width="64" height="64">Bobby Lee - email: quasar@b0b.com - gigs - CDs
Sierra Session 12 (E9), Williams 400X (Emaj9, D6), Sierra Olympic 12 (C6add9), Sierra Laptop 8 (D13), Fender Stringmaster (E13, A6),
Roland Handsonic, Line 6 Variax

Earnest Bovine · Post by **Earnest Bovine** » 19 Mar 2003 9:58 am

I certainly have problems with some chords, (what is a jazz chord?) and some days they all sound bad to me. But I do use diminished sevenths sometimes, and they sound OK. Maybe that's because I user a smaller comma (closer to ET) than you.