Stretch Tuning

[Saul Davis Zlatkovski]

It’s time to re-open this topic. I had a piano tuner come, who had stored in his strobe tuner a stretch tuning from an expert tuner. How much did he stretch it? 6th octave C was not stretched, but the B to G were lowered a few cents, the F about five cents, and the 7th octave C was ten cents lower.
The surprise was, the stretching began by 3rd octave C, at three cents, 2d octave C was about ten cents higher, and 1st octave C about 15 cents higher. 0 Octave G was 25 cents higher!
The harp sounds much better in this tuning, and it helps the regulation, which tends to run sharp in the sharps already. Increasing the space between top string and bottom string, pitch-wise, makes the harp sound bigger. It also sounds clearer. When you tune exactly to a tuner, everything is lined up and reverberating to a maximum, which is nice sometimes, but not always.
The important thing is, stretch tuning is the historic tradition. Tuning to a tuner, unless you could buy an expensive strobe tuner, was only done in regulating, and it was only around 1985 that the first Korg tuner became affordable. Which improved tuning overall, but created a false standard. I have listened to recordings and all the notes above the third octave sound flat, even though perfectly in tune with a tuner. But that’s not how the human ear hears.

[carl-swanson]

Interesting Saul. Here’s an experience I had with stretch tuning, but on piano.

Years ago a piano tuner friend of mine lent me a 1904 Steinway B(I think that’s what the model was). It had a gorgeous resonant sound. About a year later I needed to have it tuned and called my piano tuner friend, who lived in New York. He gave me the name of a Boston tuner, and the man came over and tuned it. The piano sounded perfectly in tune when he was done. But it had lost that gorgeous resonance. When my friend, the owner of the piano came to visit I told him what had happened. He went to the piano and played a couple of chords. “He didn’t stretch the octaves” he said. “I’ll work on it after dinner.” He worked on it for maybe 20 minutes and when he was done the beautiful resonance was back. I’ve never tried stretching a harp, but I may give it a try now.

[Marco Hilgeman]

Definitely interesting Saul…I think I’ll give that a try, just to hear how it will affect the harp sound and how my ears will take it. But the amount of stretching you mention from the 3d octave up, does that apply to every string of that octave, or only to the C’s you mention? And the 4th and 5th octave, are they not involved in the stretching?

[carl-swanson]

The first time I regulated the harps at the Metropolitan Opera, Deborah Hoffman(rest her wonderful soul) told me she wanted every single note exactly zeroed in on the strobe tuner so that there was no drift up or down. None at all, which is really difficult to do. I told her that normally when I regulate a harp for orchestra work I leave the upper octaves very slightly sharp. No, she didn’t want that, so I worked really hard and got every single note to sit exactly in tune on my machine(and hers). The following year when I came back to do the harps again, she told me to regulate the harps the way I normally do. She said that she had had problems being exactly in tune with the rest of the orchestra in that range, which frankly I knew would happen. Orchestra players, and in particular the violins, push the pitch sharp as they play, which leads me to a question I have always had about orchestra playing:

If an orchestra, or even a smaller instrumental ensemble, is playing without a fixed pitch instrument(piano, organ, harpsichord, harp, etc.) are they playing in equal temperament, or just intonation? And are we as listeners used to hearing two different tuning systems(equal temperament and just intonation) without even realizing it?

Years ago I was over at Symphony Hall regulating the harps for the Boston Symphony. When I took a break, I walked past a small room where a French horn player was sitting in front of a very elaborate and big strobe tuner, which had a separate strobe screen for each pitch in the octave. He was playing scales and arpeggios very slowly, watching the screen for each pitch he played to check intonation. I think he was checking to be sure he was tuning to equal temperament, which is what the machine would have shown him.

[kreig-kitts]

The best I can say from when I play flute is that they’re playing in tune, whatever that is. Apart from perhaps early music specialists trying to recreate period performance practices, there isn’t a conscious thought of deliberately playing sharper than X frequency. However, wind instruments are generally built around certain scales as far as tube length and bore and hole spacing and size, so that influences what they can do and the tools with which to do it.

People usually adjust their instruments to a fixed pitch, which can come from one of the instruments in the ensemble, sometimes a nearby piano, or a tuner or fork etc. As we play, it’s a constant listening act, which is one reason the pitch drifts, in addition to changes as the players figuratively warm up and the instruments literally warm up. Generally, the higher pitch instruments try to “listen down” in the ensemble in a tutti section, since we’re trying to build an ensemble sound. If I’m playing second, I’ll listen to the firsts if I’m usually matching an interval with them, so I’ll be more concerned about how my e-flat sounds against the first’s a-flat, or maybe I’m unison against another instrument and need to listen to them as well. Ideally, the players are aware of the piece as a whole and where they need to listen at a given moment.

In addition, players to practice with intonation as one of their goals. Our school band room had a big strobe tuner and we were encouraged to practice playing in tune on it, so this would influence the players’ internal ears and general habits as far as embouchre and air. I assume this would have been set to an equal temperament, partly so that tubas, horns, trumpets, and piccolos could all use it with satisfactory results when everybody plays together.

There are some other things having to do with wind instruments and harmonics, things like brass fanfares, that are a big can of worms and outside of my expertise as well as most people’s interest.

This article on orchestral tuning for piccolo players is a very good read on some of the tuning issues in ensembles.

@http://powellflutes.com/academy/stephanie-mortimore/articles/taming-beast%E2%80%94revolutionize-your-piccolo-intonation

[Saul Davis Zlatkovski]

I gave the C’s as a guide, the other strings would gradually rise to match the increase. The fourth and fifth octave are not stretched. It has to do with the way the ear naturally hears.

[Alyson Webber]

Carl,

As one who played horn for most of my life before adding harp (which is a wonderful relief as a wrong note you can fake to sound decent on harp, not horn), I think that he was just trying to make sure the horn was in tune to itself (there are 7 slides you can adjust in the horn BESIDES the overall tuning slide). Perhaps this is equal temperament, an attempt to keep all of the harmonics for each valve in line when playing a scale. However, as kreig writes, on a wind instrument or string instrument, the ability to adjust intonation is so extreme that I believe the true “temperament” would be that of the individual.

That is the issue I am having with harp vs wind. It drives me crazy that one string sounds good in one chord and not another. Do you folks ever find yourself tuning your harp differently depending on what piece or group you may be playing with? Do you think there are advantages to learning to tune by ear (what is the trick? octaves, fifths and fourths?) rather than electric tuner?

[Biagio]

Boscha describes the method on page 20 of Universal Harp Method. Marta Cook, bless her heart, “translated” Boscha’s rather quaint period words into something more approachable on her blog – see Best Tuning Method Ever:

http://shutupandplay.ning.com/profiles/blog/list?user=0pzata31tv1cq

If you can’t get to the link you may have to join her listserve. It’s worth doing.

In answer to Alyson I wish I had the discipline to tune by ear more often!

Biagio

[charles-nix]

As an early-intermediate player I’m most often lurking here or asking questions. But here, perhaps I can help. My 35-year “day job” is pipe organ builder–and we live in the world of temperaments and tuning daily.

Pianos are stretched because they do not produce even, regular harmonics. The stretch makes them sound better (more in tune) than tuning dead in. Each instrument may require a different amount of stretch, in different registers, to sound at its best. Many piano tuners today just use an electronic tuner, or perhaps add some standard amount of stretch, which does not create a very artistic result, as Carl noted.

I’ve had a lever harp for 15 years, and a pedal for almost one year now (thank you, Carl, for #188!). I use an electronic strobe to get close in the middle octave, then check the temperament by ear, and finish out by ear. Invariably, I find that I have stretched the trebles sharp several cents through the octaves to the top of the harp, and the basses not quite as much flat. But it all sounds exactly dead in.

No electronic tuner, even a strobe, is accurate enough to really nail the thirds, fourths, and fifths to produce a temperament that sounds good in all keys. Even with going over 2 or 3 times, on my most accurate reference strobe tuners, one can usually find some faults that can be improved by ear. And, the strobes have perhaps ten times the accuracy of any needle or lcd tuner.

Does the harp move away from this? Yes. But when it is all really solidly in tune, the entire instrument resonates and rings much better than it sounds by just tuning each string to the electronic tuner.

The attack on any plucked instrument is very sharp, decaying slightly flat. The harmonic content on a harp, while not as irregular as a piano, is not as pure as, say, a pipe organ (which, by the way, is never stretched any at all).

Alyson, I think you’re exactly right about strings and wind instruments–there is so much variation available that the performers tune in on the fly. The variation available is so much greater than even the greatest variation in any temperament that the term really has no meaning except on fixed pitch instruments.

I’ve gone on too long. Did any of this help? or just raise more questions?

Charles Nix

[Alyson Webber]

Thanks for the link, Biagio. I’ll put my over-sensitive ear to the test tonight.

Charles, Thanks for the insight. I honestly thought that all fixed-pitch instruments would be held to the same physics, but I suppose the method the sound is produced must play a big part in pitch. Now I’m going to wonder whether to tune the attack or the decay… 🙂

This topic actually brings to mind a music theory teacher that I had who, a religious man, thought that before “the fall” of man pitch and mathematics got along just fine. Our issues with temperament came about because of original sin. If that is the case, sin has at least allowed a fascinating discussion here!

[Biagio]

Ahem (the math guy clears his throat)….math and music are perfectly in tune with each other, but the occidental 12 tone scale is not in tune with itself and that is the problem.

Without going into a long very dry dissertation, picture it this way. When we strike a string (or for that matter blow on a wind instrument) our ears hear and interpret not just the fundamental but the overtones as well. The fundamental is a multiplicative function from octave to octave (middle A 440Hz, next A 880), but the overtones are not. That middle A’s second harmonic (the octave) is 880 but – whoops! – that is awfully close to the lower D’s (293.66 Hz) third harmonic which is 879 Hz. So we hear a “beat”.

Stretching is a way of having each octave pretty much in tune with itself (equal temperament) and eliminating those beats between octaves. With equal temperament in all octaves those beats would still be audible (and annoying).

By the way, a clarinet sounds different from a harp because of their different patterns of overtones, not the fundamentals.

[Janis Cortese]

Wind/string instruments also usually don’t play in a super-wide range, nor more than one note at a time. Tuning, in my opinion at least, is about compromise. When you have more than one note sounding at a time, you have compromise; that goes for ensembles as well of course.

Pianos and harps have such a huge range, and can play GOBS of notes at once, especially the piano. A single-note instrument can dance around the Pythagorean comma like a sort of moving land mine and almost pretend it’s not there; when you are playing handfuls of notes six octaves apart, the only really stone-cold proof against that moving land mine is to chop it into fine powder and dust it evenly all over the landscape. (At least, if you want to be able to modulate wherever you want in the middle of a piece.)

There’s some experimentation going on around this in the world of virtual pipe organs that fascinates me — where one can set stops to move the “sweet key” around as one plays. That would be fascinating — to start a piece in C Major and wander off to F#, and be able to adjust the tuning to sound great in both would be amazing!

In general though, I’m agnostic on the topic of tuning. It’s like speaking two languages with different ways of pronouncing an R. In French, you do it their way and it sounds good. In Welsh, you do it differently, but it sounds good in that context.

FWIW, I’m also interested in this whole “stretch” thing as well, because I noticed that I tend to like the sound of my harp better when I tune the bottom end somewhat flat and the top end dead-on. I suppose that has the same result as long as I’m the only person playing.

[charles-nix]

Janis, what you’re doing with your harp _is_ stretch tuning. And it doesn’t really hurt when playing with other instruments. The pitch variations of wind and string instruments from one player to another and the relatively short compass of other instruments prevents a practical problem in ensembles–mostly you can’t hear the small amount of stretch used in a harp with all the other out-of-tuneness going on. Unless you’re playing with a harp ensemble. ‘Course the last harp ensemble I was playing with, the struggle was to get some harpists to get the upper register even on the right note.

Biagio, I can’t follow your logic; you’re perfectly right about the third harmonic/second harmonic clash–which would produce 1 beat per second–but upper notes are stretched farther and farther sharp, which would make the 880Hz sharper, and the beats (a little) worse, not better.

I’ve understood that the main reason stretching sounds better is that the attack is always sharp, and you’re tuning the “average” sound of the strings being played. You will get a different tuning if plucking octaves together than if rolling them slightly. (On pianos, there are also many irregular harmonics which affect how the tuning sounds. We pluck in the middle of the string, so the harmonics are much more regular.)

The deviation from pitch on attack for higher notes is greater than for lower, because you’re increasing the overall tension of the string proportionally more when deflecting a shorter string. Additionally, a 5 cent pitch deviation in 7th octave C is 0.1 Hz; a 5 cent variation at 00G is close to 10 Hz. The speed of beats heard depends on the actual numerical difference of frequencies–any two pitches that are 1 Hz apart produce 1 beat per second, but 1 Hz apart at 7th octave C is half a semitone (50 cents). at 00G, 1 Hz is half a cent, which is not noticable to any ear or tuner as being “not G”.

Fun discussion! Thanks to Saul for starting it.

Charles Nix

[Biagio]

Charles, I’m not sure what logic was in that little blurb of mine. Simply observing out that mathematics perfectly describes sound waves which are continuous functions. When we introduce discrete divisions the math gets more complicated so we’ve come up with equal temperment, just temperment, etc. etc. Perhaps I should have made a distinction between pitch and frequency. In any case our statements are “in synch.”

Sonically yours,
Biagio

[charles-nix]

Biagio–absolutely.

Of course we could derail the thread into a discussion of temperament–but then we’d have to get into whether fast thirds are a detriment or a feature contributing to “key feeling”

Then there’s this wonder kicking around in my used-to-only-12-notes-in-an-octave brain that now with a pedal harp, one has 21 notes in an octave–and C# and Db can really be different. It brings to mind attempts back in the mean-tone organ keyboard temperament days when keyboards might have F# and Gb both, along with Db and C# both.

I doubt that one could vary the disc size enough to actually do that because of physical spacing. And, the instrument would be near-useless for late 19th century music that assumes equal or near-equal temperament, which is most of the harp literature.

Charles Nix

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