'just' tuning question

[Lorenzo]

All of that said, the tuning on whistles in general is not perfect, regardless of the temp. aimed for by the maker, so in the end, some part of the scale of the instrument is likely to be in tune with those around you, and some part of the scale out of tune with them. It's your job to get as close to others as you can, or their job to ignore you

I'm glad you added this. The difference is generally so minute, and there's so many variables, at some point it becomes mute, I mean moot.

With some instruments, like the concertina, maybe the temperature grew cooler and the reeds went sharp. Maybe the guitar went Just because of a warm temperature.

You've got to remember that the difference between a Just G and an Equal G (the G note below middle C) is only a "wah......wah.....wah" (3 full vibrations) in 5 seconds! Who's counting? And who can even hear them? The piano tuner has to have it extremely quiet to even know if it's right.

If you can tell the thing is badly out of tune, it's likely to be more than the difference between Just and Equal.

[Loren]

All of that said, the tuning on whistles in general is not perfect, regardless of the temp. aimed for by the maker, so in the end, some part of the scale of the instrument is likely to be in tune with those around you, and some part of the scale out of tune with them. It's your job to get as close to others as you can, or their job to ignore you

I'm glad you added this. The difference is generally so minute, and there's so many variables, at some point it becomes mute, I mean moot.

With some instruments, like the concertina, maybe the temperature grew cooler and the reeds went sharp. Maybe the guitar went Just because of a warm temperature.

You've got to remember that the difference between a Just G and an Equal G (the G note below middle C) is only a "wah......wah.....wah" (3 full vibrations) in 5 seconds! Who's counting? And who can even hear them? The piano tuner has to have it extremely quiet to even know if it's right.

If you can tell the thing is badly out of tune, it's likely to be more than the difference between Just and Equal.

Yes, and quite frankly, I seriously doubt that what a lot of ITM folks may think of as "Just" temp., is really that at all, because that's not what the scale sounds like to my ear - some of the notes are simply too flat. I suspect the Irish ear has become accustomed to it's own (traditional) scale of sorts.

In the end, I'm not certain how much any of this matters aside from understanding a bit of what's going on, and then using your own ear to play your own instrument "in-tune" with those you are playing with. For guitar, piano, and perhaps box (? I don't play one so I don't know) it's important to understand, so you can tune or have your instrument tuned the way you want or need it tuned for your applications, but for whistles and flutes, regardless, you've got to blow or cross finger or halfhole your way to where you need to be. Yeah, it's easier to get there if you pick the right tool for the job, but all whistles that I've played have had some inherent tuning flaws somewhere in the scale - it's just the nature of the instrument.

Pipes....... well, like you say, they're never in tune with anything or to any scale, and we need not concern ourselves with them



Loren

[Loren]

Hey Chas, are you reading this thread? Has it helped you to understand the tuning choices made on that flute?



Loren

[Mitch]

I spent a lot of time on the physics of harmony, got pretty bored with it and went back to playing music.

Just temperament is realy only useful on a whistle if you are only ever going to be playing one key - if you cross finger for the 4th note major Ionian(diatonic major), a just instrument is going to be unhappy.

It's all about how waves co-incide as they work together. For instance, play one note, play it's octave and the octave "peaks twice for every "peak" of the other, the other "harmonies" yield an integer proportion ( 1:3, 1:4, 1:5, 2:3, 2:5, etc etc). In an acoustic environment, the sounding of a note will cause harmonically tuned structures to "resonate" - play by themselves, if you ever tuned a guitar, you will know the importance of damping the strings that you are not tuning or they will "muddy" the sound by resonating and make the tuning go wierd.

Interestingly, a tuned string or column will resonate even if the initiating note is only "close enough" our ears work the same, we can get-away with slight out-of-tunenesses". Perfect harmonies have a natural logic that makes us comfortable and at-rest, dissonance is something we can also use to stop the audience from being at-rest (dance or be moved for instance) harmonies on strange proportions have interesting emotional effects. Pianos are not tuned to either a just or even temper - they are tuned with each of the 2 or 3 strings slightly off-centre to a roughly even temper - this creates a long-beat dissonance that gives the piano its great full-bodied sound - also why pianos tend to swamp and ruin pure-toned performances and make a joke out of ITM. FOr this reason, be a bit careful using "Phase delay" effects such as phasors and flangers (guitar guys!) the phase efex unit was made to mimic the 3-note piano dissonance - great for 3-piece guitar bands.

I had demonstrated to me once, a cheasy little electric organ thingy called the "Archefoon" it had 4 or 5 rows of square keys driving a very simple set of oscilators - with the first row being just temper and the ascending rows on fractional intervals. Some JS Bach played on the first row sounded like th crappest elevator music you ever heard, while played using the specific temper, sounded absolutely divine.

It all comes back to your ear - once it's trained-up enough, go looking for the in-between stuff, feel how it works, and use it where you feel it needs to be - listen for how others are using it. Without your ear/emotional system in the loop and the musical journeys you've taken, it's all just noise and rubbish.

Whistles are amazing little things for getting all this in-between stuff, is it any wonder it grabs us so much.

[Whitmores75087]

At this web site you can hear the difference between just and equal. It's noticeable, but nothing to get excited about.
http://www.wmich.edu/mus-theo/groven/compare.html

One fiddler explained this whole thing to me this way. Musical sound is like a piece of string, but it's not a straight string. It's curved. To make notes you can do it one of two ways. You can either:
A: cut the curved string into pieces of equal length (just temperament, the old way). Everything sounds very harmonious, but when you try to bang a big chord with both hands on a piano it's quite a bit off (to a musician's ear, anyway).
B: Draw a straight line under the curve, mark the straight line in equal lengths, draw a perpendicular up to curve and cut it there. Each piece will be slightly different length. When you play those big chords on the piano they sound a lot better, but there's a very slight dissonance throughout the music. Not usually enough to notice. (equal temperament, the new way).

I may be looking at this completely wrong, but it works for me.

[Lorenzo]

At this web site you can hear the difference between just and equal. It's noticeable, but nothing to get excited about.
http://www.wmich.edu/mus-theo/groven/compare.html

Here's an experiment you can do with that web site. Take a mandolin and tune one of the A strings so that it is perfect to the Just D chord they are playing. Then tune the other A string to the Equal D chord. Then, play the two A strings at the same time on your mandolin. I tried this several times to make sure I had it right. The two strings played at the same time produce about 5 beats per second. That's way too much. I know the 5th, D to A, in that sequence shouldn't sound anywhere near that far off. The 5th in the Equal temperament is only flattened enough to produce 3 beats in 5 seconds. The 5th they are demonstrating has been flattened to about 5 beats in one second. It even sounds bad to the ear. So, I think something is wrong there.

Here's good experiment that demonstrates why Just doesn't work with instruments that produce chords...

• (piano) C, G, D, A and E; it being necessary to go over these fifths before we can make any tests of the complete major chord or even the major third. Now, just for a proof of what has been said about the necessity of flattening the fifths, try tuning all these fifths perfect. Tune them so that there are absolutely no waves in any of them and you will find that, on trying the chord G-C-E, or the major third C-E, the E will be very much too sharp. Now, let your E down until perfect with C, all waves disappearing. You now have the most perfect, sweetest harmony in the chord of C (G, C, E) that can be produced; all its members being absolutely perfect; not a wave to mar its serene purity. But, now, upon sounding this E with the A below it, you will find it so flat that the dissonance is unbearable. Try the minor chord of A (A-C-E) and you will hear the rasping, throbbing beats of the too greatly flattened fifth.
  
  So, you see, we are confronted with a difficulty. If we tune our fifths perfect (in which case our fourths would also be perfect), our thirds are so sharp that the ear will not tolerate them; and, if we tune our thirds low enough to banish all beats, our fifths are intolerably flat. source

[Jerry Freeman]

Here's good experiment that demonstrates why Just doesn't work with instruments that produce chords...

Your premise here is misplaced.

Again, the only reason for equal temperament is to create an instrument that can be played in any desired key. You can most certainly tune a piano to just intonation, and I've posted links to soundclips of such pianos in a previous discussion. The chords played on such a piano sound wonderfully clean and rich. However, when you do that, the piano will be limited to one or only a few keys.

Best wishes,
Jerry

[Bloomfield]

... But it is true that modern ears are attuned to equal temperament, and many singers and instrumentalists stick to it as a matter of course, especially because pianos are used so often as a pitch reference.

Yes. Absolutely right. Hearing is habitual.

[jim stone]

At this web site you can hear the difference between just and equal. It's noticeable, but nothing to get excited about.
http://www.wmich.edu/mus-theo/groven/compare.html

One fiddler explained this whole thing to me this way. Musical sound is like a piece of string, but it's not a straight string. It's curved. To make notes you can do it one of two ways. You can either:
A: cut the curved string into pieces of equal length (just temperament, the old way). Everything sounds very harmonious, but when you try to bang a big chord with both hands on a piano it's quite a bit off (to a musician's ear, anyway).
B: Draw a straight line under the curve, mark the straight line in equal lengths, draw a perpendicular up to curve and cut it there. Each piece will be slightly different length. When you play those big chords on the piano they sound a lot better, but there's a very slight dissonance throughout the music. Not usually enough to notice. (equal temperament, the new way).

I may be looking at this completely wrong, but it works for me.

This is very helpful. The whole thread is helpful. Thanks all.

[Lorenzo]

Again, the only reason for equal temperament is to create an instrument that can be played in any desired key. You can most certainly tune a piano to just intonation, and I've posted links to soundclips of such pianos in a previous discussion. The chords played on such a piano sound wonderfully clean and rich. However, when you do that, the piano will be limited to one or only a few keys.

By Just, we mean either the 3rds, or the 4ths and 5ths, are pure through the temperament octave. Just only has one problem. The last interval will be off. If the 3rds are pure, then last interval will be off by about 40 cents. If the 5ths are pure, then you can't hit the A chord while playing in C (within the same octave) unless you develop a special taste for dissonance.

Just would be limited to one key, and the player couldn't hit the one "wolf tone," (that is, howls like a wolf it's so bad) --the one sharp interval that is naturally built in to the octave with Just tuning. When the last interval of pure 3rds, within the octave, comes out 38-42 cents sharp (howls like a wolf), you know you've forgotten to flatten all the fifths equally. But, if you can get past that one interval, without hitting it (w/o hitting the A chord when playing in C), you can move smoothly into the next octave, up or down, w/o any dissonance. If you move too far away from the center of the keyboard, like Bach noted, you'll want a more well-tempered tuning while playing in that same key you started out with. The further you get from the center, the more warped the math becomes.

[Jerry Freeman]

Larry, you've got this conceptually hashed up.

You're conflating the use of the circle of fifths construction that generates the scales of successive keys (C, G, D, etc.) with the use of just intonation's exact harmonic intervals, which do not generate pitches that can be used to build scales for successive keys. The circle of fifths approach is based on the idea that you should be able to use exactly the same set of pitches across different keys, which is why you must flatten each fifth by three beats per five seconds or you get wolf notes.

With just intonation, there's no circle of fifths, no attempt to use pitches from one key to generate other keys, and no wolf notes. You don't play in other keys because the pitches needed to play other keys in just intonation would be nowhere on a just intoned keyboard.

Best wishes,
Jerry

[fluti31415]

Orchestra players do not use equal temperment. I have actually been in situations where I was required to change the pitch of a sustained note midstream, becuase the surrounding harmony changed, and my note changed its function (e.g., from the 3rd of the chord to the 5th of the chord) in the harmony.

Of course, if you're playing with an instrument that can't be tuned (or can't be readily tuned on the fly), like a piano, harp, or percussion instrument, you use whatever tuning that instrument is using, which is probably tempered.

[kfg]

With just intonation, there's no circle of fifths, no attempt to use pitches from one key to generate other keys, and no wolf notes. You don't play in other keys because the pitches needed to play other keys in just intonation would be nowhere on a just intoned keyboard.

See the so called "tranposing" harpsichord. Because the instruments were not equal tempered you couldn't simply move your hands a fourth to play in tune in the two keys and the instruments actually required the addtion of two more strings per octave to play in both keys, in tune.

The harpsichord being large and expensive made this a reasonable choice over having to buy and maintain two instruments, despite the added expense of the double manual instrument.

If you've got WhOA, however, you're always looking for an excuse to pick up few more whistles.

KFG

[Jerry Freeman]

I would like to back away from the discussion of keyboard tunings.

I'm annoyed because this seems to me to be taking the discussion down a sideline that requires more effort than I want to expend. However, looking further into the question, I will have to concede to Lorenzo that instruments designed to play chords don't lend themselves to just intonation. Instruments that play single notes in concert with other such instruments are capable together of creating any desired chord, cleanly in tune, and that's the main point I've been trying to make. Specifically, that quite a lot of music is played in just intonation without anyone's giving any thought to whether what they're doing is equal or just. From Wikipedia:

In practice it is very difficult to produce true equal temperament. There are instruments such as the piano where tuning is not dependent on the performer, but these instruments are a minority. The main problem with equal temperament is that its intervals must sound somewhat unstable, and thus the performer has to learn to suppress the more stable just intervals in favour of equal tempered ones. This is counterintuitive, and in small groups, notably string quartets, just intonation is often approached either by accident or design because it is much easier to find (and hear) a point of stability than a point of arbitrary instability.

Best wishes,
Jerry

[Cayden]

I will have to concede to Lorenzo that instruments designed to play chords don't lend themselves to just intonation.

depends on the number of keys you want to play in doesn't it?