Dirty-South Blues Harp forum: wail on! > just & equal temprament, what's the diff?
just & equal temprament, what's the diff?
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John M G
113 posts
Apr 13, 2017
7:55 PM
What is the difference between Just and Equal temprament.
What is best for Blues?
Cheers JG
Gnarly
2152 posts
Apr 13, 2017
8:03 PM
In a nutshell, some harmonicas (most of the Suzuki line, for example, and almost all chromatics) are tuned to Equal temperament. That way, all notes played (without bending) are in tune with other instruments.
Just and its variations make it so that the chords are in tune.
I think Just sounds good with blues.
Adam Pritchard
122 posts
Apr 14, 2017
12:26 AM
Out of interest, what is a piano tuned to?
The Iceman
3094 posts
Apr 14, 2017
4:46 AM
Pianos = equal temperament MOST of the time

Pianos can be tuned to any temperament
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The Iceman
Jim Rumbaugh
1251 posts
Apr 14, 2017
6:32 AM
my opinion

Just intonation gives you delicious chords just like Gnarly said. It's good for 2nd position playing and blues.

But when I do traditional melody tunes,(1st position) like Camptown Races, Etc., equal temperament (my Suzuki harps) sound better to me. My Honers have a few notes that just sound slightly out of pitch.

If you have a bad ear, they will all sound alike. If you have a good ear, you CAN hear it.

FWIW
A while back I returned one of harps. I tuned the 1.2.3.4 blow and draw to just intonation, then 5 through 10 to Equal. That fit my styles of playing. If I do just intonation all the way to 10, I don't like what it does to my 3rd position playing on holes 4,5,6.

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theharmonicaclub.com (of Huntington, WV)

Last Edited by Jim Rumbaugh on Apr 14, 2017 6:38 AM
hvyj
3264 posts
Apr 14, 2017
6:54 AM
The way I look at it, ET puts you in tune with other musicians. JI puts you in better tune with yourself when you play chords but out of tune with the rest of the band, especially in positions above third. JI does work very well for the choo-choo train thing, though.
dougharps
1405 posts
Apr 14, 2017
7:20 AM
The "diff" = difference tones

Equal Intonation is good for on-pitch single note playing and renders abrasive, harsh chords without difference tones.

Just Intonation makes for rich chords with difference tones adding a low note to make the chords sound full. Some notes will sound flat when played individually with other instruments.

Some players reportedly have separate sets to be used depending on what is being played.

I prefer a compromise tuning that smooths out chords with some difference tones evident, and doesn't have the extreme flat sounding notes of some Just Intonation tunings when single notes are played. When you are tuned to 442 or 443 and play Compromised Intonation harps it sounds pretty darned good. It is a compromise!

Pat Missin pages on equal, just, and difference tones:


Equal and Just Intonation

Why Just Tuning sounds so good
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Doug S.

Last Edited by dougharps on Apr 14, 2017 7:22 AM
hvyj
3265 posts
Apr 14, 2017
9:16 AM
In positions above third, there aren't a lot of chords available. And in ANY position, the relatively primitive chords (including difference tones) and chord fragments available don't always work well with non-blues musical material, which means you can fit harp to a wider variety of material if you don't play chords. So, it all depends on what kind of stuff you want to play and what positions you play it in. 19 limit JI is supposed to be pretty flexible.

Last Edited by hvyj on Apr 14, 2017 9:20 AM
arzajac
1824 posts
Apr 14, 2017
9:20 AM
"Pianos = equal temperament MOST of the time

Pianos can be tuned to any temperament"

The difference between a piano and a harmonica is that when you strike a low key on an acoustic piano, the sound will reverberate through the strings and you will get many series of overtones and harmonies - these are created by the other strings vibrations. That's why a triad played in the low register of a piano sounds mushy - too many competing overtones and loss of harmony.

Harmonica reeds are more independent and to achieve harmony, you need to adjust the pitch of the individual notes.

It's interesting that to get two notes in harmony (octave, tonic-third or tonic-fifth for example) you need a fair amount of precision. But in Equal Temperament, notes can be off by several cents and nobody will even notice.

When tuning ET, you can often come "close enough" while tuning for chords requires you be right on target or else it will not sound in harmony. A chord in harmony sounds bigger than the sum of its parts.


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Custom overblow harps. Harmonica Combs and Tools.
hvyj
3266 posts
Apr 14, 2017
9:36 AM
Octave stops/splits will ALWAYS sound big and generate a difference tone.
barbequebob
3405 posts
Apr 14, 2017
10:11 AM
@Jim Rumbaugh --- The just intonation you're talking about would be 7LJI, where 5 & 9 draw is tuned 27 to 31 cents flat, but what you could do as an alternative that is tune to 19LJI, which is basically the same as 7LJI except 5 & 9 draw is tuned 1.5 cents sharp.
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Sincerely,
Barbeque Bob Maglinte
Boston, MA
http://www.barbequebob.com
CD available at http://www.cdbaby.com/cd/bbmaglinte
nacoran
9429 posts
Apr 14, 2017
11:20 AM
This link has a nice primer on Temperament and how it developed over time, but it doesn't have the sound samples anymore.

http://www.slate.com/articles/arts/music_box/2010/04/the_wolf_at_our_heels.html

Basically, it's a math problem. If you pluck a string it sounds one note. If you cut the string exactly in half and pluck it again you get the same note exactly one octave higher. You can do that over and over.

The problem is that certain wavelengths line up nicely with others. Mathematically they fit together and make nice smooth sounding chords. Others don't.

There is also a simple mathematical relationship between each note in a scale. If notes follow that spacing they sound in tune.

Unfortunately, the relationship that gives you the nice smooth sounding chords isn't quite the same as the relationship that gives you nice in tune sounding single notes, so when tuning systems are designed they have to decide whether to go for great sounding chords (Just Temperament) or notes that sound in tune (Equal Temperament) or some compromise in between.

Historically they tried all sorts of different schemes. Some of them even tried different solutions in different octaves or in different keys. Historically this meant different keys had much more distinct sounds compared to modern keys. With electronic keyboards it's much easier to play around with some of these old keys so we can hear how some of the classics are 'supposed' to sound. (Which is why it's so sad that the links are broken in the article.)

For us harp players it means if you are going to be playing a lot of melodies you may want a harp that leans towards Equal. If you are just going to be chugging, lean towards Just. If you are going to be mixing, a Compromise Tuning maybe the ticket. Really though, the difference can be small enough that you may have to train your ear to be good enough to hear which is which. You may hear that they are 'different' but may not be able to put your finger on it.

It's probably worth, at some point in your playing, to try a couple different temperaments, because ultimately your own personal preferences are what make your sound your own.

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Nate
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STME58
1959 posts
Apr 14, 2017
12:19 PM
I found out about the book "HOW EQUAL TEMPERAMENT RUINED HARMONY (AND WHY YOU SHOULD CARE)" by Ross W. Duffin from the article Nate linked to. I find the book fascinating. I really appreciate the dilemma of the Pythagorean comma that gives rise to the problem of temperament. On a related note, a few years ago it was discovered that the hand written curls at the top of Bach's "The Well Tempered Clavier" is actually a code, well know at the time but lost, that described the temperament to tune the piano to to play the pieces.

Here is a pianist demonstrating temperament on a room full of pianos tuned to different temperaments.
John M G
114 posts
Apr 14, 2017
10:25 PM
I play predominantly 2nd and 3 rd positions, occasionally 1st, but mostly single note stuff in first such as "Trouble in Mind" which only uses a couple of chords
Do a lot of split octaves especially in 3rd.
chromaticblues
1767 posts
Apr 17, 2017
9:41 AM
STM58 you bet me to it. I was going to explain that most concert pianos are not Equal Temperament.
groyster1
2925 posts
Apr 17, 2017
2:30 PM
all the old great blues harp players....played either marine band or old standby....tuned to 7JI....to me those harps sound better by far.....rich chord sound....but I like my golden melodys for what they were intended to play.....melodies
Gnarly
2157 posts
Apr 17, 2017
3:33 PM
If you play 12th, you probably don't want to tune to Just--the note that gets flatted the most is the root!
F on a C harmonica.
Short of that, a good harmonica player can play in tune on an equal tuned harp--but some of the two note chords may sound off.
DanP
331 posts
Apr 17, 2017
5:23 PM
I think (someone correct me if I'm wrong) that all Hohner harmonicas are now tuned Compromise with the exception of the Golden Melody which has always been tuned to Equal Temperament. Can someone tell me if there are still any stock harmonicas that come in Just Temperament?
Gnarly
2158 posts
Apr 17, 2017
5:31 PM
The Fabulous comes in Equal or Just--
Get your wallet out . . .
1847
4072 posts
Apr 17, 2017
5:59 PM
YOU could try one of these fabulous harmonicas
.600_439660165
STME58
1960 posts
Apr 17, 2017
7:51 PM
chromaticblues, that is news to me. I thought that outside of demonstrations of historical tunings, most pianos are tuned to equal temperament. It would make sense that if you are playing 18th or 19th century pieces you might use a tuning contemporary to the piece. It sounds like you may have some first hand experience in the matter, is that the case?
DanP
332 posts
Apr 17, 2017
8:04 PM
After checking Hohner's website, I think I can answer my own question. To paraphrase Hohner: The Hohner Blue Midnight, part of the MS-Series, features the classic "Chicago Style" tuning from Hohner's vaults. So I assume that means Just Intonation.

Last Edited by DanP on Apr 17, 2017 8:10 PM
chromaticblues
1769 posts
Apr 18, 2017
7:24 AM
STME58 Concert pianos are actually tuned ET within the octave and then the next octave starts 2 cents higher. Each octave being 2 cents higher than the last. So it really isn't true ET! I have tried tuning harps this way. It actually works pretty good. The beating on the octaves is soft and slow. I thought it sounded cool. It isn't great for Blues, but for Pop or Rock it might?
barbequebob
3406 posts
Apr 18, 2017
8:58 AM
Just to make things clear, there isn't just one single version of just intonation. The one version of it that had been used on diatonic harps for many decades is 7 limit just intonation, which does have 5 & 9 draw tuned really flat, but there are tons of others but the other two that have been used over the years are 19 limit just intonation, which was first used by Huang when they came out in 1982 and 5 limit just intonation, which is only used on minor key tuned harps. The Blue Midnight uses 19 limit just intonation, and that version is the most versatile of them all.

Pianos have been tuned to equal temperament since the 1700's, but however, they're also tuned to what's referred to as stretch tuning, meaning that for each octave above or below where middle C starts, it's 2 cents sharper. For example, the first octave higher or lower than middle C is tuned 2 cents sharp, then the following octave higher or lower is another 2 cents sharper (4 cents sharp), etc., and where the hammer strikes the string allows ET to work properly with the instrument and if it's placed anywhere else, ET doesn't work because of the problem with the upper harmonic overtones.
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Sincerely,
Barbeque Bob Maglinte
Boston, MA
http://www.barbequebob.com
CD available at http://www.cdbaby.com/cd/bbmaglinte
Gnarly
2160 posts
Apr 18, 2017
10:10 PM
I have been using my iPhone to do tuning, and have a few apps I like.
But Joe Spiers was recommending the iStroboSoft, and since he usually knows what he is talking about, I sprang for it.
Turns out it has some great temperaments, automatic retuning for just and minor just (along with some others I have not been using).
You can easily set the offset to 442 or whatever (437, who cares).
Haven't heard from Joe lately, hope he is OK.

Last Edited by Gnarly on Apr 18, 2017 10:12 PM
STME58
1962 posts
Apr 18, 2017
11:43 PM
To really get a handle on the dilemma that is temperament, you need to understand just a bit of physics. To sound a note an octave up, you double the frequency. If you think of a sin wave going up down up and another one going up down up down up at the same time, you see they line up perfectly both hitting zero points at the same time every two cycles of the higher note. A perfect fifth is similar but with three waves fitting over two so that at the beginning and end of three cycles of the higher note, everything is zero. This gives you pleasant sounding cords with no beating. The problem comes when you build scales using octaves and fifths. For convenience lets set G to 100 Hz, you double every octave so the G 7 octaves up is 12800hz. Now lets start with the G at 100 and go up 3/2 to D, a fifth, and get 150 Hz, then another 3/2 to A at 225 and so on around the circle of fifths and back to G at...12974.6??? That's messed up!! G should be the same whether you go up by octaves or by fifths, but it's not. This difference is called the Pythagorean comma. How you deal with it to make a scale that works, basically how you divide the error up among the notes, is what temperament is. Equal temperament is dividing the error equally among all 12 notes. There are no nice exactly 3/2 fifths in equal temperament, but there are no horrible clinkers for some fifths either.

Last Edited by STME58 on Apr 18, 2017 11:45 PM
eetechTom
26 posts
Apr 19, 2017
9:34 AM
Great discussion, I have a lot to learn about this topic. Seems like it would be helpful on instructional videos to mention the tuning of the harp being played. It never seems to be listed from my experience.
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Fil
298 posts
Apr 19, 2017
9:59 AM
Thanks STME58. I think I'm finally starting to get it, or at least some of it....
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Phil Pennington
The Iceman
3096 posts
Apr 19, 2017
1:52 PM
Being a piano tech, I'm pretty familiar with tuning schemes. The "stretch tuning" as discussed above was not anything I experienced, was taught or used. This 2cents/octave is interesting, but not part of my real world experience.

Stretch tuning that I used was used as I moved away from the middle octave tuned ET. Using octave tunings, I would begin to "stretch" the octaves to where they were just beyond total exact octaves (no beats). My approach was to allow the upper note of the octave drift slightly sharper in order to begin a pulse, or beat, but not complete one. I don't believe that this is a 2 cent measurement, but can understand how some might think of it as such.

The stretch tuning is used to compensate for our human ear, which hears those higher octaves/notes as "flat" when tuned spot on without stretching.

I was very active in the years before portable tuners were invented, so developed an ear approach and philosophy of tuning on my own. When those computerized small tuners came out, I found that I could tune quicker by ear and also could make compensations to the piano I was tuning so that it would sound at its best, even with all the inherent not perfect aspects of that vibrating string. Adhering totally to a computerized tuning program eliminated the individual piano's voice in favor of a general one size fits all type approach.
Tuning is an art and not a science.
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The Iceman


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