Wikipedia has a good page about Partch's 43-tone scale. It's geeky fun to construct jazz chords by picking intervals from Harry Partch's charts.

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Bobby Lee (a.k.a. b0b) - email: quasar@b0b.com - gigs - CDs, Open Hearts
Williams D-12 E9, C6add9, Sierra Olympic S-12 (F Diatonic)
Sierra Laptop S-8 (E6add9), Fender Stringmaster D-8 (E13, C6 or A6) My Blog

[This message was edited by b0b on 07 June 2006 at 02:26 PM.]

On pedal steel, I eventually gravitated to a Meantone tuning, which, roughly speaking, is somewhere between JI and ET. It sounds more pure than ET, but allows about twice as many usable intervals/chords as JI.

This caused me to do some RESEARCH.

I couldn't find exactly what I was looking for (looking for Mike Perlowin's summation of his basic tuning method) but here's a post by chas smith following b0b's thread about tempered tuning.

quote:

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I tune my E9 neck to a sort of "hybrid", that being a combination of Just and Tempered. For instance, most of the 3rds are Just and the 7th string, F# has the same number of beats with the B as it does with the C#.

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http://www.larrybell.org/id32.htm

E# -5x
A# -4x
D# -3x
G# -2x
C# - x
F# 0
B + x
E +2x
A +3x
D +4x
G +5x
C +6x

b0b, when you say "not really JI" tuning was culprit for that D-F m3 problem, does that mean the fix is tuning to true JI and only using that said beatless m3 interval for your diminished?..or something like this..

[This message was edited by James Winwood on 07 June 2006 at 09:35 PM.]

Earnest and I disagree on the use of meantone for E9th. He uses it, I don't. He always sounds better than me though, so maybe he's right. I use meantone for C6th, but I can't seem to adjust my ears to it on E9th.

I tune likely closer to Ernest's method.

I play a lot of jazz chords and bigger voicings.
Both on C6 and E9
I get a "by ear general good place" for several large voicings.
Based on a tunered reference E note.

And from then on it's just a slight tweak over the playing period.

Neither straight up ET,
nor what I see put forward as "correct JI"
seems to work for me.

You can tune the 1st and 7th string to the fifth string, after all the open triads are tuned. Now On both the A and B pedal, lower those strings slightly until they are in tune with the pedal down combinations. Also on A & B pedals, and the E's to F lever, lower the D string slightly for the same conclusion.

You may choose as I have not to do everything I listed above because of knowing other positions where the same chord voicing can be played perfectly in tune using other strings. If you use them all, there is virtually NO harmonic limitations and you get to keep the sweet sound of JI.

Paul

[This message was edited by Franklin on 08 June 2006 at 05:25 AM.]

Note that Paul also says "I nudge my 3rds around 1 or 2 beats sharp of JI". If he didn't do this, the C# would be so low that there would be no way to get the F# low enough to be in tune wioth C#, and high enough to be in tune with B.

quote:

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With the meantone tuning, do you just tune all the notes (open and pedal/knee) to those said numbers and leave it at that? Are there any other issues with this, like cabinet drop?

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As x gets bigger, thirds and sixths sound purer, while fourths and fifths get less pure. At x=3.5 the major thirds are beatless, but I don't like this for two reasons:
1. Fifths and 4ths are worse.
2. If the major third gets any narrower than pure, and it will sometimes because steel guitars are mechanically imperfect, it will sound bad.

At x=2.5, major thirds are about 4 cents wider than pure, and fifths are about 4 cents narrower than pure. Everything sounds pretty good, so this is a good compromise.

I sat with a German Carillion design team
at AES in Amsterdam one year.
Listening for 3 hours about how they planned
to create and "time" electronic real bell carillions
for differing musics.

They would analize the music involved,
and either time songs with clashing intervals till
they were slow enough not to beat
horribly on an existing bells system they were updating.
It was both a midi system, that could be sequenced
AND played by a keyboard in realtime,
with servos calibrated to midi volume levels,
and a traditional hand pull system.

But they were also working with a foundry to
design modern bells with differing harmonics
than traditional, to play some songs normally
too disonant for traditional carillions.
These were added as alternate bells,
duplicating the notes of existing bells.

They were generally leaning to several
variants of Meantone tunings.

A VERY deep group of thinkers.
They had a demo system in a room,
and the difference between trad
and their special bells was very apparent.

Meantone was their only choice for this.

[This message was edited by David L. Donald on 09 June 2006 at 04:52 AM.]

For example, the 3rd of the IV chord (A pedal) is tuned flat (of ET). That gives a sweet JI IV chord. But that same note is 6 of the scale, and is used as the root of the relative minor chord (C#m for open E9). Well, the 6 of the JI scale is supposed to be flat. This makes it so when it is played as the relative minor root, the minor 3rd of that chord is suitably sharp for a minor 3rd, because it is tuned straight up ET as the 1 of the scale.

This also works for many jazz chords. That A pedal note above also gives a good I6 chord. So on both E9 and C6, the flatted 6 of the scale works good as the 3rd of IV, the root of VIm, or the 6 of I6. Likewise, on E9 if you tune strings 7, 5, 2, 1 to a V chord, the flat 3rd of that chord (string 2) also works good as the maj7 of the I chord, which is also supposed to be flat.

So the traditional way to tune E9 by ear gives both a good JI scale, and good JI main chords, even some jazz chords. You tune your 1 note (E) to a tuner. You tune the rest of the open strings of the E chord by ear to JI. You mash the A and B pedals, and you tune those stops to the E strings, which are now the 5ths of the IV chord. Then you tune strings 7, 2 and 1 to the open 5th string as a V chord. String 9 is tuned as the minor 3rd of the Vm chord with string 5 as the root, and strings 7 and 1 as the 5ths. Then you tune your other pedals and levers, always using some chord with an open string, and tuning the pedal and knee lever stops to the open strings, which never get changed after tuning the open I and V chords. For all the main combinations the intervals can be made JI, but some of the chords will not be right over the fret, for example the C# chord with the F lever.

Now we come to the diminished chord (F lever alone) and augmented chord (A and B pedals with F lever). I’m a little bit baffled by these chords, because I don’t know what the proper JI intervals should be for a diminished chord. If you take a diminished chord from equally spaced minor thirds of a JI scale, the intervals between these supposedly equally spaced notes are not identical. Is that the way a JI diminished chord is supposed to sound? Or are the diminished intervals supposed to be identical, which can only be achieved with an ET scale? Same question for the augmented.

What I have noticed is that diminished and augmented chords sound reasonably good whether they come from a JI or ET scale, apparently because they are dissonant chords to begin with, and any additional dissonance added by the tuning method doesn’t seem to matter the way it would on a straight major or minor chord. It seems like 6ths, 7ths, 9ths, 13ths, b5s, and maj7ths work out okay when taken from a JI scale.

So the bottom line is that tuning to a JI scale by tuning the I, IV and V chords JI works out good for the main straight chords, and many jazz chords. And jazz chords such as diminished and augmenteds, also work okay, because any dissonance caused by the JI scale is acceptable. So JI works okay for E9 jazz. JI also works okay for simple C6 jazz using open strings, bar movements and a few basic pedals. But if you keep adding pedals and knees and strings to C6, you get strings and stops that are used for different intervals in 3 or more chords, and you run into unresolvable conflicts. Tampered JI tweaks and meantone systems can help with these, as the posts above demonstrate. And if you have a complicated C6 setup and have to move closer to ET, that seems more acceptable, because jazz chords embrace dissonance, so the inevitable dissonance of ET is less noticeable or objectionable.

I personally play a lot of my jazz from the A pedal minor position on E9/B6 S12U. This has the roots on strings 12, 9, and 5, and has pentatonic possibilities and blue notes all across the strings. Because this is simply the relative minor of the E9 tuning (C#m), it works out well tuned JI, for jazz or anything else. From bottom to top the intervals are: 1 b3 5 1 b3 4 5 1 b3 5 2 4. The A pedal toggles between the b7 and the 1, and a vertical knee raises the 4s to b5s. Another way to look at this is that the A pedal turns a uni into a 12-string E6 neck. From bottom up the intervals are: 6 1 3 6 1 2 3 6 1 3 M7 2. The A pedal toggles between 5 and 6. The vertical lever raises the 2s to b3s, and separate levers lower the 1 to M7 and m7. Either way you look at it it’s a killer position for jazz, but more blues jazz than swing jazz. And it’s basically all JI with a little tampering.

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Student of the Steel: Zum uni, Fender tube amps, squareneck and roundneck resos, tenor sax, keyboards

[This message was edited by David Doggett on 09 June 2006 at 02:52 PM.]

I believe Ernest tunes all the thirds sharp to JI.

...that F lever seems to be the real sticking point for me; yes, as the 3rd of a major triad w/ pedal A it can be tweaked no problem, but w 8raised, 6 5 and 2 lowered a 1/2 to make the diminshed chord...

Love, Sleepless In Boston

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http://www.johnmcgann.com
Info for musicians, transcribers, technique tips and fun stuff. Joaquin Murphey transcription book, Rhythm Tuneup DVD and more...

If a player prefers the sound of JI, yet the E's to F lever is the problem and a compensator is not an attractive solution for that player. There is A harmonic solution which is to completely omit the 8th and 4th raise and play strings 5 6 and 9 in the same diminish positions. And any combination of 5 6 3 and 2 lowered a 1/2 tone works. Everywhere a dominant seventh is found, that voicing, substitutes for the diminish chord.

To sound like the diminish chord, The 8th and 4th raise really isn't needed when the band plays the diminish chord?

Partial harmonies can be the most expressive. Keyboardist Bill Evans made that abundantly clear in his approach to chords. To play a partial harmony, we need to play the strongest notes of any given chord. Once the bass player plays, the chord becomes crystal clear.

Paul

[This message was edited by Franklin on 11 June 2006 at 09:35 AM.]

This is getting interesting, and exciting to be around when it's being published.

I'm going to have to go over my piano concerto collection and see if I can tell which notes are not played, and what would happen if they were.

EJL

quote:

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Diminished 7th chords by nature allow any note to be the root, since the chord itself splits the octave into 4 equal parts...

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Better to listen to what notes Bill Evans doesn't play. Concertos, they play so many.

I know jazz guitar players who strive to just use a triad aproach, that is just using triads super imposed to get whatever tension or color they need for chord playing.
I feel we have a leg up on them in this or a similar interval related approach, considering the ability to tune at or near JI and use of the bar. This line of thinking has become increasingly attractive over time as my ears have developed to hear - and want to hear - things really in tune.

I agree that choosing certain string group and not others due to "wolf intervals" (lol) is something that seems to have to be accepted to some point. I can see clearly the point of arguement, is having to deal with this outweighed by the JI benefits, and my ears say I will have to deal with this.

Part of the fun in playing in a jazz context is playing more than 3 notes, although it is true that you can define a chord with just the 3rd and 7th- there are times when you also want the "tensions" on top- like to realize the A7#5#9 in the bridge of "Yesterdays"- Bill Evans would voice it with 3 and b7 in the bottom, then #9 and #5(the melody note) on top. You could disregard the #9, but then, it just isn't the same sound, and sometimes [i]less is less[i]. If you check out any of the excellent Bill Evans Trio transcription books (there are 3 put out by Hal Leonard) you'll see there is a lot more going on that 3 note voicings most of the time...

So, for this A7#5#9 we'd be looking at C# G C F. I might find this on strings 7 raise a 1/2, 5, 3, 2 raise a 1/2.

On the E9, I don't think I could get this chord "in tune" with the tweaked/sweet triad tuning...

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http://www.johnmcgann.com
Info for musicians, transcribers, technique tips and fun stuff. Joaquin Murphey transcription book, Rhythm Tuneup DVD and more...

If a bass guitar was tuned to match the notes in the middle octave of the piano it would be sharp to the band. Each instrument should be tuned to the octave that matches its sonic range. The steel guitar and the violin are both in the same melodic range. The orchestra violins tune to the octave above middle A (440) that octave sets at about 441 to 443 depending on who tuned the piano. 442 is an average that always works.

Paul

[This message was edited by Franklin on 12 June 2006 at 09:57 AM.]

If you're curious, try tuning the E open to 442, forget the tuner after that. You should hear a pleasant difference especially when you experiment using some open strings in combination with fret positions.