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Meantone temperament (Page 3)
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The Steel Guitar Forum
Pedal Steel Archive
Meantone temperament (Page 3)
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| This topic is 3 pages long: 1 2 3 This topic was originally posted in this forum: Pedal Steel |
| Author | Topic: Meantone temperament |
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Bobby Lee Sysop Posts: 14849 |
posted 19 May 2001 09:10 AM
There's a tuning method called meantone temperament that was very popular in the early days of keyboard instruments. The idea was to shrink the fifths a little bit to make the thirds sound more true. There's a catch, though - some key signatures sounded very out-of-tune. This isn't a huge problem on pedal steel. We can move the bar up or down by a fret or two to get the key signature with the correct intervals. Nobody needs to play the E9th in C at the 7th or 9th fret, even though the notes are available there. We go to the 8th fret where it sounds best. I used meantone temperament on my F Diatonic Tuning and it sounded very good for most kinds of music. It gets sort of funky, though, with 12-tone classical or jazz. Those forms sound best in equal temperament, in my opinion. I've never used meantone on the E9th because I'm so comfortable with my own temperament there. Also, I wasn't sure how to resolve the cabinet drop issue with meantone (the F Diatonic tuning doesn't have much cabinet drop). Meantone shrinks all of the fifths by the same amount. Let's call it X. To get real pure thirds, X would be about 3.75 cents flat of an ET fifth on the tuner scale. I started out using 3 cents and later settled on 2.5 cents because it's easier to see on the tuner (half a notch). If my tuner used Hz markings, I'd probably use 2 cents because each Hz reprecents about 4 cents of tuning. The F# note is the "wolf" of the E9th. It wants to be flat for the A chord and sharp for the B chord. To devise meantone for E9th, we set the F# to the center of the scale and march around the circle of fifths in both directions, adding or subtracting X cents with each step: G +5XApplying this to an E9 copedent chart, we get: | pedals | knee levers |If a guitar had no cabinet drop, I think that this would sound pretty good at X=2.5 cents or X=.5 Hz. I'm not sure how to adjust it for cabinet drop, though, and that's what scares me. Has anyone here ever used meantone temperament on the E9th? ------------------ [This message was edited by Bobby Lee on 19 May 2001 at 09:13 AM.] |
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C Dixon Member Posts: 5912 |
posted 19 May 2001 11:02 AM
I have never knowingly used "meantone". I am not sure I even know what it is. I do use a combination of JI and ET on my D-10. Examples are: JI.... 1. 3rd and 6th strings. 2. 2nd string. 3. A pedal, 5th and 10th strings. 4. E lever, 4th and 8th strings. 5. F lever, 4th and 8th strings (JI with A pedal). 6. RKR, 2nd and 9th strings to C#. 7. A pedal 1st and 7th strings. (compensators). 8. C pedal, 4th and 5th strings. ET.... 1. 9th string. 2. Knee lever raising 1 and 7 a half a tone. 3. 1st and 7th strings. 4. knee lever lowering 5th and 10th strings a half a tone. 5. 5th and 10th strings. 6. 4th and 8th strings. 7. B pedal, 3rd and 6th strings. 8. RKL, 6th string (lower whole tone). Where I get into real trouble is certain combinations are NOT right. Examples: 1. Splitting the B pedal with lowering the 6th string a whole tone. In order for the A7th to sound rich, the E minor chord does not sound good. And vice/versa. 2. The F lever used alone does not sound right when trying to get a pretty diminished. I have NO solution for this, except to go straight ET and like b0bby says that makes all strings sound out of tune with each other, more or less. Is "meantone" a way of splitting the difference b0bby? carl |
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Bobby Lee Sysop Posts: 14849 |
posted 19 May 2001 01:52 PM
Not really, Carl. It's a different system. It's sweeter sounding than equal temperament (ET) because the thirds don't have as many beats, but it makes those pretty thirds at the expense of the fourths and fifths which have more beats than in ET. Fourths and fifths are real close to pure in ET, and of course they're pure in just intonation (JI). In meantone (should we abbreviate it 'MT'?) the fourths and fifths sound worse than in ET, but the thirds sounds better. How much better/worse depends on the value of X. On the diatonic steel, meantone sounds a lot better than ET to my ears. I couldn't figure out any other way to tune the diatonic so that all 7 scale positions sounded in tune. MT and ET were the only tuning systems that worked at all. ------------------ [This message was edited by Bobby Lee on 19 May 2001 at 01:56 PM.] |
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Sage Member Posts: 525 |
posted 19 May 2001 06:55 PM
Bobby, I read your work and just marvel at you, man. Might be a while to get us up to speed on MT though. Watch out- we'll start getting a reputation as the hottest forum in the world for tuning disscusions. We'll have to chase all the banjo players away with an old C string  . |
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chas smith Member Posts: 3168 |
posted 20 May 2001 12:46 AM
Hi Bobby, me again. When organs were tuned in MT way back when, they would start with say the lo C and tune the G above it to a Just perfect 5th, 3/2, then tune the D above that to a just p5, then the D an octave below, then the A above that to a just p5, then the E above that and so on through the entire cycle of fifths until it came back around to the A again, and it would be sharp. If we use A-220 as our starting point, the just E a perfect 5th, 3/2, above that is E-330. The tempered E, 12th root of 2 to the 7th power is E-329.627, not too much difference, but when we go through the entire meantone cycle of perfect 5ths, 3/2, when it gets back to A, instead of being the octave, A-440, it's A-446.003. This difference is called the Comma of Dydamus. |
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Bobby Lee Sysop Posts: 14849 |
posted 20 May 2001 08:21 AM
Chas, you know too much! |
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John Kavanagh Member Posts: 378 |
posted 20 May 2001 10:03 AM
Once, long ago, I thought I understood this stuff. Since my reference books are not here, I'll dredge what I can out of memory for now, proving once again that a little knowledge can be a dangerous thing  Back in the days when I was hanging out with harpsichord and organ players, I think I learned that there's more than one meantone tuning. The idea is that you take the Pythagorean comma and spread it out among the fifths. Quarter-comma mean tone is when you Anyway, my classical quartet, which includes viola da gamba, harpsichord, guitar, and violin, has opted for ET because the guitar has fixed frets and it's so awful for his unisons with the harpsichord to be out of tune. My gamba's frets are adjustable, and that electronic tuner I bought for my steel guitar (which I DON'T tune in equal temperament) sure came in handy - ET is one tuning you just can't do by ear. What I tell the Early Music Police is that we use twelfth-comma meantone tuning, which is, of course, equal temperament. If they think about it and then laugh, we're both childishly happy because we all know we're clever [This message was edited by John Kavanagh on 20 May 2001 at 10:09 AM.] |
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chas smith Member Posts: 3168 |
posted 20 May 2001 01:39 PM
Viola da gamba - steel guitar, early music police - country fundamentalists, hemi-semi-demi-quavers. Pythagorean commas - Dydamus commas, wom pom pa loopa, ba lom bam boom quote:Yeah, me too, it's been 25+ years since I've thought about this stuff which is why it's so much fun. I have a program in my computer that has a library of scales and there must be about 900 scales in there almost all of which I've never heard of. Then again the Table of Elements has more elements in it than when I was in school. |
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Bobby Lee Sysop Posts: 14849 |
posted 20 May 2001 04:40 PM
quote:Now I get it. 12 tone ET divides that comma Chas talked about into 12 equal segments, which is the difference between an ET fifth (700 cents) and a just fifth (702 cents). The tuners we use have this adjustment built into them. The "X" that I talked about above is in addition to the 2 cents built into the tuner. So if you use X=2 cents with an electronic tuner, you get 1/6 comma meantone. Why do it at all? The main reason tis that the major and minor thirds are still a long ways from pure harmony in ET. By taking the MT equation further we can get better sounding thirds. The sacrifice is that we can no longer play in all 12 keys at any fret. That's no big deal (just move to a different fret), but there's another problem. Certain styles of music have come to include the free modulation feature of ET. Jazz and modern classical music make use of diminished, augmented, and other advanced chords that simply don't work in other tuning systems. ------------------ |
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David Pennybaker Member Posts: 1203 |
posted 21 May 2001 10:16 AM
quote: I'm glad you do. Because my head hurts again. And I'm an engineer, so I'm SUPPOSED to be able to understand this stuff and not be able to play well. (The second part I can handle just fine ------------------ |
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