#31
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It sounds to me like you’ve come up against the basic physics that led to Well-Tempered tuning. With instruments which have fixed tuning of individual notes, they cannot be in perfect tune in all keys at once. This applies to quite a few instruments, but not all. Violins have no trouble at all.
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-Raf |
#32
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It is equal temperament which is our modern solution to shifting keys within one piece of music, which was demanded by the composers. Equal temperament detunes each interval so that (in theory) the error is so small you can't hear it. Bear in mind that we, people born in 20th century, have been exposed almost exclusively to equal temperament, so we hear it as "correct". It's only when you hear a string quartet or unaccompanied singing that you hear perfect intervals. There is a definite sweetness to the sound which cannot be maintained as soon as any fixed pitch instrument joins the fun. These days there is a large movement to recapture old tunings for older music, with various claims about how it affects the psychology of the listener. It's a big debate and there's loads about it on the internet. So, feel sympathy for your piano tuner..... you're paying him/her to tune your piano and he/she is faced with the task of detuning it in such a way that you won't notice! Not a straightforward task at all I can tell you😀 Nick |
#33
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We had a blind piano tuner when I was a kid, who would spend a couple of hours tuning all 230 strings of our old upright. He could barely play a note himself.
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Faith Mars FRMG Faith Neptune FKN Epiphone Masterbilt Texan |
#34
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A couple of short (I hope) points.
As was pointed out the interval of a 'perfect' fifth has a frequency ratio of 3:2. Your 7th fret 'harmonic' divides the string into three equal parts, and gives a pitch that is a musical 12th (an octave and a fifth) above the fundamental. Thus the 7th fret partial on the low A=110 Hz string gives 330 Hz~ E. You could construct a scale that way. Start with the A, and get E a 12th higher. Drop that down an octave and use that to get B, drop down an octave again, and so on. Each time you drop down an octave you are dividing the frequency by two. So, you do this 12 times and you're almost back to the original pitch. Almost. The problem is that you've been multiplying a frequency by 3 every time, and then dividing it by 2 every time. There is no way you can start with a number, multiply it by three and divide it by two any number of times, and end up with the same number. That's ultimately why it's impossible to construct a scale on 'pure' intervals; it's just math folks. The system we use is '12-tone Equal Temperament'. The difference between the note you start with and the note you end up with in constructing the 'pure' scale, the 'Pythagorean comma', is divided up into equal size pieces (musically speaking) and spread out in all the intervals. This has two results. One is that all the semitones are musically equal in size, so that the frets are straight. The other is that each major key is 'out' in the same way to the same degree as every other, so you can modulate freely from one key to another without it sounding different. Apparently this doesn't work well on pipe organs. Unlike strings air columns produce lots of 'perfect' harmonics. The lowest note on the organ will have harmonics that are supposed to be in tune with the fundamentals of the highest notes. In ET they won't be, and it shows. Organists use unequal temperaments, where the semitones can all be different in size to get around this. Bach favored one such scheme that was called 'Well-temperament', which was, apparently, not the same as the 'Equal temperament' we're used to. I have heard recording made on instruments in what purports to be Bach's well-temperament, and they do sound different. Guitar players tend to use one or another 'sweetened' tuning that makes the usual guitar keys sound nicer. That's what most of the 'crooked fret' schemes do, too. The first dulcimers I made used '1/4 comma mean tone' fretting. They really sounded sweet until you tried to play along with a guitar. |
#35
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Interesting point about pipe organs Alan. Now that I think about it, you can hear those harmonic overtones and the consequent tuning issues pretty clearly when you listen to it, which gives the instrument a unique kind of wonky sound. That would have been very relevant to Bach given all the organ pieces he composed. I always thought it was interesting that it was the Well-Tempered Clavier (not piano, or organ, or harpsichord) so I guess his version of tempered tuning could have been intended as a compromise for any keyboard instrument.
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1943 Gibson J-45 Martin Custom Shop 000-28 Authentic Aged 1937 Voyage Air VAOM-4 |
#36
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When pipe organs were mentioned in this discussion, that made wonder about harmonicas. Since they are often used to accompany guitars, what tuning method do they use?
There are three different types of tuning available: There is just intonation which makes chords sound in tune. Tempered tuning is used just like in other instruments such as piano which makes melodies sound in tune. Compromised tuning is the third and it is a compromised version of the first two methods. Jerry |
#37
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When tuning, if you expect a good and consistent result is having a tuner that can truly do the job. Most clip-on tuners get you in the ballpark, but aren't dead-nuts accurate. There are a few exceptions (i.e. Peterson strobo-tuner). I prefer to use something like a Korg CA-40 which has an on-board mic and plug-in capability (often in conjunction with a Korg Pitchblack for confirmation). One of the things that should be recognized with the JT tuning beyond partial correction of equal temperament is also compensation for string deflection. When strings are plucked they tend to go a bit sharp. The lower strings will suffer more from string deflection than the higher strings. JT tuning isn't a perfect system, nor does it help every guitar. My experience with JT tuning is that my Taylor guitars do not do very well with it. My Martin likes both standard and JT tuning, but it will sound different, one tuning from the other. My Alvarez Yairi and MIJ Epiphone both seem to benefit the most from the slighly altered tuning.
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Assuming is not knowing. Knowing is NOT the same as understanding. There is a difference between compassion and wisdom, however compassion cannot supplant wisdom, and wisdom can not occur without understanding. facts don't care about your feelings and FEELINGS ALONE MAKE FOR TERRIBLE, often irreversible DECISIONS |
#38
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Vin, can one not mitigate string deflection simply by tuning to fretted strings rather than open strings? Unlike the JT tuning, it would be specific to the guitar.
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Purfle Haze Recreational guitar player |
#39
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There are a number of ways to mitigate string deflection. One way is to simply play lighter. And yes, you're right. As I said, JT tuning kills the mojo on my Taylors, is great on my Epi and Yairi and is just different but acceptable, but not necessarily better on my Martin. Each individual guitar is different. But again, regardless of whether you use standard tuning or JT tuning, it is important to accurately tune as close to dead-nuts on as possible.
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Assuming is not knowing. Knowing is NOT the same as understanding. There is a difference between compassion and wisdom, however compassion cannot supplant wisdom, and wisdom can not occur without understanding. facts don't care about your feelings and FEELINGS ALONE MAKE FOR TERRIBLE, often irreversible DECISIONS |
#40
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The other half of the problem is how consistently a particular instrument is able to achieve those pitches. Compensation at nut, saddle or both is used to counter the increase in string tension that causes a fretted string to play sharp. |
#41
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This is a huge subject. Many books have been written if you really want to get neck deep in the subject. I like:
How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross W. Duffin | Oct 17, 2008. Be thankful you don't play a wind instrument. They operate from the overtone series and the player is constantly "tweaking" notes to blow them in tune. You can't build an equal temperament trumpet. For guitar the major thirds are the ones that easily offend my ear. I'm not going to re-tune the guitar for every new key, but I sweeten the thirds on the 1st and 2nd string when they call to me.
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Keith Martin 000-42 Marquis Taylor Classical Alvarez 12 String Gibson ES345s Fender P-Bass Gibson tenor banjo |
#42
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That's the battle that we face. I guess it is a matter of knowing your instrument and having a tool that is accurate enough to get you closer than just in the ballpark. Also tuning has a lot to do with which instruments you're playing besides.
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Assuming is not knowing. Knowing is NOT the same as understanding. There is a difference between compassion and wisdom, however compassion cannot supplant wisdom, and wisdom can not occur without understanding. facts don't care about your feelings and FEELINGS ALONE MAKE FOR TERRIBLE, often irreversible DECISIONS |