equal tempered and tuning

Construction and repair of Classical Guitar and related instruments
Astra Piotr

equal tempered and tuning

Post by Astra Piotr » Wed Dec 13, 2006 9:56 pm

Hello Delcampers,

Could you shed some light on the question related to guitar tuning. (I know, tuning again... :? )

But in one of the articles suggested here in one of the threads, the concept of 'equal tempered" scale was explained. From the article mentioned, I discovered that equal tempered is different from just tempered and the perfect fifth, for example, is not exactly perfect. :roll: :roll:

So starting from A (220 000hz) a perfect fifth should be 330000 but in fact it is 329.707942hz. The question is if it affects tuning with the electronic tuner. From what I understand the tuner shows real perfect fifth (in this case E-330 000hz) and thus the quitar is not well tuned according to the mathematical solution of "equal tuning", even if the display shows the correct note. Shoul the tuner be somehow adjusted or maybe the difference is so tiny that it can be neglected ??
:? :o :aide:

guitarrista

Post by guitarrista » Wed Dec 13, 2006 10:24 pm

The tuner you have should be equal-tempered tuner. These would typically show not frequencies but note symbols (letters), along with some info about cents +- that you are off when comparing with string pitch. When they show you an E4 it is already on the equal-tempered scale so it corresponds to a frequency of 329.63 Hz.

bones

Re: equal tempered and tuning

Post by bones » Wed Dec 13, 2006 11:08 pm

Astra Piotr wrote:Hello Delcampers,

Could you shed some light on the question related to guitar tuning. (I know, tuning again... :? )

But in one of the articles suggested here in one of the threads, the concept of 'equal tempered" scale was explained. From the article mentioned, I discovered that equal tempered is different from just tempered and the perfect fifth, for example, is not exactly perfect. :roll: :roll:

So starting from A (220 000hz) a perfect fifth should be 330000 but in fact it is 329.707942hz. The question is if it affects tuning with the electronic tuner. From what I understand the tuner shows real perfect fifth (in this case E-330 000hz) and thus the quitar is not well tuned according to the mathematical solution of "equal tuning", even if the display shows the correct note. Shoul the tuner be somehow adjusted or maybe the difference is so tiny that it can be neglected ??
:? :o :aide:
Tuners are good for giving you a single reference pitch after that learn to use and develop your ears, they are the best musical tools nature gave you. Accomplished guitarists tune their strings 'sympathetically' to take account of the effect of how fifths, thirds and octaves 'beat' relative to the chords they are playing, for instance you might tune the guitar so that a chord of E major in first position sounds true but then C major might sound like the g string is a little flat so you make adjustments, flattening and sharpening here and there, the better your ear gets the more critical this becomes, I find hearing out of tune, Western music can make me feel physically sick or become quite aggresive. Take your time to tune up spending a few minutes getting it near perfect will help you to enjoy your practice sessions more, try to keep the room temperature consistent too.

Azalais

Post by Azalais » Thu Dec 14, 2006 12:44 am

Some keys and or chords sound especially painful if you do not cross check the octaves that occur in particular pieces. A tuning fork is often more useful than the electronic tuners, which are great for getting "close" but hardly ever "just right". The tradition way to tune is to start with the open A and then to work back and forth to get all of the other strings tuned by ear in relationship to the reference A. (and then check a few chords and octaves, or "sing" the tones instead of using the tuner)

Bones mentioned a physical reaction... and I have to agree... after listening to lots of lute and guitar music, hearing modern equal tempered pianos can really set my nerves on edge :oops: Hearing the "beats" can even cause a feeling of vertigo or nausea, especially if you listen with headphones.

Alexander 1985

Post by Alexander 1985 » Thu Dec 14, 2006 8:21 am

Azalais wrote:...after listening to lots of lute and guitar music, hearing modern equal tempered pianos can really set my nerves on edge :oops: Hearing the "beats" can even cause a feeling of vertigo or nausea, especially if you listen with headphones.
Why is that? :o And why there are beats if the piano is equally tempered?

Azalais

Post by Azalais » Thu Dec 14, 2006 9:01 am

The piano just sounds "different" and mildly disturbing to me. They sound harsh and tense in contrast to the music that I have grown used to hearing.

When one of my own strings gets slightly out of tune, (my baroque guitar has eleven very low tension strings and a very thin top, some gut and some wound, that seem to sharpen overnight and "beat" first thing in the morning in protest!), I get very distracted till I fix it, and it sometimes sets up odd sympathetic vibrations or overtones or air turbulence that can be quite strong till I get everything smoothed out, and the guitar "warms up" to body temperature. I am so used to listen for strings that might be out of tune that the sound bothers me more than it should when I hear them in recordings or the middle of a concert, or when I am playing.

Astra Piotr

Post by Astra Piotr » Thu Dec 14, 2006 8:24 pm

Is it true that when strings are old it might be impossible to tune them correctly ?? :roll:

Astra Piotr

Post by Astra Piotr » Thu Dec 14, 2006 8:29 pm

F
or instance you might tune the guitar so that a chord of E major in first position sounds true but then C major might sound like the g string is a little flat so you make adjustments, flattening and sharpening here and there, the better your ear gets the more critical this becomes
Sounds a very good exercise but in my case, I'm afraid, the process can be endless :( :(

bones

Post by bones » Thu Dec 14, 2006 8:41 pm

Astra Piotr wrote:F
or instance you might tune the guitar so that a chord of E major in first position sounds true but then C major might sound like the g string is a little flat so you make adjustments, flattening and sharpening here and there, the better your ear gets the more critical this becomes
Sounds a very good exercise but in my case, I'm afraid, the process can be endless :( :(
LOL no it's not endless Astra just practice you will get better. Certainly you should change strings relative to how much time you practice for , the more you practice the more you will need to change the strings, I play a lot, a heck of a lot in fact and once a month is about right sometimes more. If you roll one of the bass strings over you will see the metal has become flattened where it impacts the fret in pretty much the same place, this cause intonation problems, compound that six times all over the guitar and you realise how important it is to change strings. If we could buy a guaranteed perfect set of strings every time and our guitars were made with the frets accurately placed to microns of a mm then we would have less of a problem. Factor in temperature to the equation and we quickly see that a guitar has the potential to permanently be out of tune just like the ones my pupils bring to me every lesson :roll: :D
So buy new strings regularly and learn to hear the 'beating' of out of tune strings. Perhaps one of the resident luthiers can explain the problems of making guitars with regard to tuning, James I see you are here, guess who I am?

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James Lister
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Post by James Lister » Thu Dec 14, 2006 10:55 pm

Hi Bones,

Yes, I've guessed - it was one of your posts that mentioned me that led me to this forum - for which I thank you!

As for the problems of making guitars with regard to tuning, there is a limited amount that the luthier can do. Fairly early on I started using a jig for cutting the fret slots, so that at least I know the frets are in exactly the right place, and I fine tune the position of the leading edge of the saddle so that the 12th fret harmonic is in tune with the 12th fretted note. Beyond that, we are limited by the nature of equal temperament (and the quality of the strings).

I have heard of someone making guitars made with slightly different fret positions for each string, but haven't been able to find any more information. I can't really work out why this should help, and it sounds like a nightmare to make. Has anyone else come across this?

James
James Lister, luthier, Sheffield UK

Azalais

Post by Azalais » Thu Dec 14, 2006 11:28 pm

Wim Hoogewerf has one, and there are a couple of threads about his guitar... start here:
viewtopic.php?t=9208&start=0&postdays=0 ... able+frets

bones

Post by bones » Thu Dec 14, 2006 11:33 pm

jmdlister wrote:Hi Bones,

Yes, I've guessed - it was one of your posts that mentioned me that led me to this forum - for which I thank you!

As for the problems of making guitars with regard to tuning, there is a limited amount that the luthier can do. Fairly early on I started using a jig for cutting the fret slots, so that at least I know the frets are in exactly the right place, and I fine tune the position of the leading edge of the saddle so that the 12th fret harmonic is in tune with the 12th fretted note. Beyond that, we are limited by the nature of equal temperament (and the quality of the strings).

I have heard of someone making guitars made with slightly different fret positions for each string, but haven't been able to find any more information. I can't really work out why this should help, and it sounds like a nightmare to make. Has anyone else come across this?

James
Hi James
I think most of us musicians are interested in the instruments we play, Bach was to some extent an organ repairer, builder and designer, specifying the thickness of woods and metals to create new stops. I've always been fascinated by how guitars are made and in particular pitched but there are only so many hours in a day so I just leave it to those like yourself to inform me when I have a question, I have a load more by the way. See you soon with Adelina as she will be called. 8)

charles dodgen

Post by charles dodgen » Fri Dec 15, 2006 2:39 am

I have heard of someone making guitars made with slightly different fret positions for each string, but haven't been able to find any more information. I can't really work out why this should help, and it sounds like a nightmare to make. Has anyone else come across this?
Hi,

Here’s a bent, unbroken fretting method. Different temperaments other than equal temp. are available as well as an "optimized equal temperament fret layout", where the bent frets are used to individually compensate each note for the varying degrees of sharpening due to fretting stretch to achieve as close to 12th root of 2 semitones as possible. The fret shapes and positions are not derived from a strict formula, but through empirical measurements for each neck. And I think your right, James. A few places on the site mention the painstaking time and effort that goes into the execution.

This site has a lot of good information on guitar intonation and compensation along with their inherent difficulties, different historical temperaments, etc.

http://guyguitars.com/eng/index.html

From this site, there is a link to the "True Temperament" site that explains the fretting method, reasons for it and a few video samples, although they seem to be focused on electric guitars. One of the more interesting temperaments that they have emulated is the Bach-Lehman temperament, which is a well-temperament that was extrapolated from a series of seemingly ornamental loops on the cover of Bach's original manuscript of The Well-Tempered Clavier, Book 1. Some musicologists and historians believe that Bach drew these loops to illustrate his tuning method. There’s a video example of this temperament played on an electric guitar by Paul Guy, one of the cofounders of this fretting method. He’s fingerpicking some jazzy progressions, which sound nice, but I wish he’d play some Bach. There is a link to Dr. Lehman's site as well where you can read all about Lehman’s temperament derived from the WTC manuscript (others have done this before him) and hear some sound samples of Bach’s music played in the “Bach” temperament, some by Dr. Lehman, on pipe organ and harpsichord.

Charles

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James Lister
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Post by James Lister » Fri Dec 15, 2006 11:01 am

Thanks Azalias, Bones and Charles - that's given me quite a lot to look into and think about - don't think I'll be offering variable/adjustable frets just yet though.

James
James Lister, luthier, Sheffield UK

Azalais

Post by Azalais » Fri Dec 15, 2006 11:07 am

You could always offer gut frets... :wink:

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