In isolation I get it it, but as part of an ensemble. Once the pianist is doubling bass lines, or playing melodies high up, they are flat or sharp respectively.
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Perfect 5ths' aren't Really Perfect
- Thread starter KarateChris
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The railsback chart you posted is showing the tuning of the Fundamental only.
If it were showing the average of the fundamental and overtones, adjusted for their respective amplitudes, it would be a straight line. (if the piano is tuned properly)
If it were showing the average of the fundamental and overtones, adjusted for their respective amplitudes, it would be a straight line. (if the piano is tuned properly)
Right, at the bass end a piano string isn't really a single "note" any more. The harmonics aren't exact multiples of the fundamental, they're sharper (progressively sharper as they go up). So you've got a tradeoff, you can tune so the fundamental is more in tune, or so the higher harmonics are more in tune. The decision to stretch tune is a decision to prioritize the tuning of the higher harmonics.
Note this is all true of plucked bass guitar strings as well. I wonder which part of the overtone series the typical tuner focuses on.
But the fundamentals are tuned flat to sharp. The 2nd and 4th overtone are tuned to it too. A bass string has the same overtone series, but not the range. So if the pianos fundamental is tuned flat, they sure a bass guitar/Upright should too.
Bass guitar strings are not (typically) struck on harmonic nodes, so mostly only the fundamental is ringing. There are definitely overtones, but not as apparent as when a sting is ringing from a harmonic. If you could watch a high speed video of a bass guitar sting, you would see a single wave going back and forth between the bridge and the fret. If you watched a piano string, you would see at least two waves bouncing back and forth between the bridge, capo bar and also smashing into each other.
A bass string does not have the same overtone series as it is not ringing from a harmonic node.
Edit
Piano and bass guitars, and all string, wind, all vibrate harmonically as opposed to en-harmonically (Membranes), so they all have the same harmonic series. Odd and even. But they have different amplitudes and of these harmonics creating the different tones, plus a different attack sound depending on what driving the vibration. If you strike at a node, it amplitude decreases for that harmonic. but with a bass, that strike point varies, depending on if we pluck/pick towards the bridge, or the neck and how long we have made the string by frettng.
This is my understanding of harmonics, Am I amiss so far?
Piano and bass guitars, and all string, wind, all vibrate harmonically as opposed to en-harmonically (Membranes), so they all have the same harmonic series. Odd and even. But they have different amplitudes and of these harmonics creating the different tones, plus a different attack sound depending on what driving the vibration. If you strike at a node, it amplitude decreases for that harmonic. but with a bass, that strike point varies, depending on if we pluck/pick towards the bridge, or the neck and how long we have made the string by frettng.
This is my understanding of harmonics, Am I amiss so far?
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I don't understand why striking the string somewhere other than a harmonic node would damp the harmonics.
If anything, I'd expect striking at a point to decrease the amplitude of any harmonic with a node at that point.
Pretty certain most of what you actually hear from a bass note is harmonics.
As the bass player, I try to get the keyboard player to not use his left hand. Seriously, I have been in churches that both the piano and organ were used simultaneously, and the piano tuner did not stretch the tuning as much as a concert piano so it would coordinate better with the pipe organ, which being wind and not strings, with truer overtones, does not suffer from inharmonicity as much as a piano.
Most of what you hear from a bass note is an overtone, but not a harmonic overtone. A harmonic overtone requires the sting to be divided by a node, (ie touching your finger to the 12th fret) A piano hammer strikes the string at the node.
Plucking at different points of a string to get a different tone has been around as long as there have been stringed instruments. For example, in classical guitar, you will see multiple notations of technique to get different tones out of the same string depending on the position, angle, and release of each note on each string, what we call articulation in other contexts.
The purpose of the stretch tuning to deal with inharmonicity deals with the fundamental physics of string vibration over a bridge. A string does not vibrate laterally alone, parallel to the bridge saddle. The string also vibrates perpendicular to the bridge, and all around, so that the string is actually rolling on and off the bridge saddle microscopically. This actually creates a differential in the vibration of the string, causing the overtones to go slightly sharp, depending on the string. That is why pianos only have the core of the bass strings go over the bridge, in order to minimize this inharmonicity, and why Dr. Kemp puts about 1 centimeter of extra windings near the bridge end of bass guitar strings, to damp this inharmonicity of overtones, as you can see in his traces in his published work.
No all strings do not vibrate the same way are not all harmonic.
The ideal string is harmonic (i.e. has overtones frequencies which are exactly integer multiples of the fundamental). In order to be ideal, strings have to infinitely thin and infinitely bendable.
Real strings depart more or less strongly from the conditions of ideal strings and therefore only approximately harmonic.
Bass strings are not very stiff (they can be bent rather easily), and a not rather harmonic. The E string is thicker than the G string and less harmonic. That's is why the same note played on the G string has a brighter tone and a greater pitch clarity if is played on the A or E string.
Piano strings are very thick and stiff, which makes them quite strongly inharmonic (more so on un upright piano than on grand).
Where did you hear that? I'm genuinely curious where this idea is coming from.
The harmonic series is infinite, so, sure, any given hammer strikes near the node of *some* partial. But I've never heard that piano makers all place the hammers at the node of some particular partial.
Harold A Conklin Jr: Piano design factors
Ok, I guess I'm wrong. I had always thought the hammers were specifically located to make the string ring harmonically. Thanks for sharing that.
Perfect 5ths' aren't really perfect, or are they?
On my musical journey I have encountered the terms "Perfect 5th" and "Perfect 4th". I am teaching myself to read music, studying music theory and learning a lot. I understand, describing the 4th and 5th notes of the scale as "Perfect" is because they are the same in the major scale and the minor scale.
I know that, for stringed instruments (especially piano) 4ths and 5ths aren't tuned perfectly. This is because of even temperment. 4ths are tuned narrower than perfect and 5ths are tuned wider. If tuning non-stringed instruments (like a pipe organ) the 4ths and 5ths can be tuned perfectly.
My point/rant? This can be confusing for people learning music theory. Those intervals aren't really perfect, stop calling them that!lol!
Am I wrong? Please educate me.
I am a Registered Piano Technician so I have a bit of knowledge on the theory of tuning systems.
When you say "describing the 4th and 5th notes of the scale as 'Perfect' is because they are the same in the major scale and the minor scale.", I think you are referring to the intervals? Well, the 6th and 7th are unchanged in harmonic minor and the 2nd is unchanged in natural minor. It's an interesting observation but someone has correctly said they are called perfect because of their consonant sound. (As far as we know. There is a lot about the theory of music that seems very odd because the language is so old)
Now, the unison and octave are called perfect as well, (PU and P8) and they too are consonant. It is also interesting to note that in the equal-tempered system, (the most common tuning system for instruments and pianos) the PU and P8 are beatless, the P4 beats around 1 bps, the P5 around 0.6 bps, but the M2/M3/M6/M7 all beat much, much faster.
"4ths are tuned narrower than perfect and 5ths are tuned wider." Close. P4 is wide and P5 is narrow. Here is a video I made to explain.
Equal Temperament — How to Tune Pianos
"If tuning non-stringed instruments (like a pipe organ) the 4ths and 5ths can be tuned perfectly."
I think you are referring to inharmonicity. Pipe organs don't have any so the octaves can be tuned so that all the partials line up but the fourths are still wide and the fifths; narrow.
Pianos have inharmonicity; the higher partials are sharp from what is predicted by the Harmonic Series.
(See The Harmonic Series — How to Tune Pianos)
Therefore, when we tune octaves to sound good, the upper note is a little more than double the lower note's frequency. This produces a curve known as the Railsback Curve.
I hope that was helpful.
P.S. Should have read all the posts before posting. Sounds like there's a lot of people know this stuff already.
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The term that refers to any interval that does not beat is "Pure", not perfect.
Yes, you can if you use "Check Intervals", which piano tuners do.
Take D4 and A4 for example.
The check note is F3, a M6 below the bottom note of a P5.
Play F3 with D4, then F3 with A4.
Each will beat at A5.
If the beats are the same speed, the interval is pure (i.e. when you play D4A4 there will be no beating.)
In equal temperament piano tuners tune (or check) the fifth so the M10 beats slightly slower than the M6, making (or confirming that) the P5 is indeed narrow.
I.e. in this case, F3A4 would beat slightly slower than F3D4.
In jazz voicing, we actually leave them out (the fifths and the octave. I.e. Dm9 = F-C-E. The bass plays the root and the fifth provides nothing interesting, as you say.
The difference is small. When playing with a piano, and you are listening (and on a fretless) and care, you are probably lowering it a bit without knowing.
In reality, most orchestras are scrambling intonation wise. That's why small professional wind ensembles, like the trombone group someone mentioned, can sound so much more amazing - because they each tweak as they go.
