Guitar tuning and temperament.

[muttley600]

2 to the 1/12 power is the ratio for 12 Interval Equal Temperament. . If I could print it how it is displayed on my calculator that may help. That is also the ratio of fret spacing on a guitar. My experiment was out of pure curiosity and my interest in science. At the time I was in college for Electrical Engineering and thought it was an interesting exersize.
VP

VP I know how to calculate the fret spacing on a guitar to achieve 12et. That is not really of importance to this thread as yet. I was hoping to move on to the two methods that are used to calculate fret spacings on a guitar in a later post. Could I ask that you wait until then before we discuss it. Thanks.

 

[Victory Pete]

OK I'll try and make it a bit easier. The first question I asked was in response to you this part of your post

My question was..



So what are you advocating here? Do you tune all the instruments? How do you use your Peterson V-Sam Tuner? What are the advantages of that particular tuner? Most importantly how do you tune those instruments for your clients?

I will rephrase the other questions I raised when we have dealt with this one if it is easier for you to respond in this fashion.

I want all the instruments to be tuned as accurately as possible within my means. This also means it can be repeatable at any time in the future. I use the Peterson as Equal Temperament. I have tried the other tunings in it and find the ET is the most versatile and dependable. The VSAM is very accurate, it is a virtual strobe tuner with a display that simulates a true strobe. I compare it to other electronic tuners and when the others show "in tune" there is still more adjustment to be made with the Peterson. I dont always do the actual tuning myself, I would show the musicians how to read it and tune themselves.
VP

 

[muttley600]

I want all the instruments to be tuned as accurately as possible within my means. This also means it can be repeatable at any time in the future. I use the Peterson as Equal Temperament. I have tried the other tunings in it and find the ET is the most versatile and dependable. The VSAM is very accurate, it is a virtual strobe tuner with a display that simulates a true strobe. I compare it to other electronic tuners and when the others show "in tune" there is still more adjustment to be made with the Peterson. I dont always do the actual tuning myself, I would show the musicians how to read it and tune themselves.
VP

VP with the greatest respect, did you read the first post. It sounds to me that you are talking about doing something that has nothing to do with the subject of this post.

How are you using this tuner to achieve 12ET?

Why is it important that you have a "VSAM"?

How does this relate to a method of tuning your guitar by ear using a single note as reference that gets the best from your guitar?

 

[Victory Pete]

VP with the greatest respect, did you read the first post. It sounds to me that you are talking about doing something that has nothing to do with the subject of this post.

How are you using this tuner to achieve 12ET?

Why is it important that you have a "VSAM"?

How does this relate to a method of tuning your guitar by ear using a single note as reference that gets the best from your guitar?

Once again these are my opinions, observations, perceptions and practices. Of course I can tune a guitar by ear, and yes it is hard to purposely detune your guitar slightly to achieve ET, but I feel the most accurate way for me and the people in my studio is to use a tuner.
VP

 

[muttley600]

Once again these are my opinions, observations, perceptions and practices. Of course I can tune a guitar by ear, and yes it is hard to purposely detune your guitar slightly to achieve ET, but I feel the most accurate way for me and the people in my studio is to use a tuner.
VP

VP we are not dealing with your opinions, perceptions and practices here.

This thread was the result of a request made directly to me to provide some factual concise and accurate information on the subject of how to best tune your guitar to avoid common issues that are commonly experienced by many guitar players.

I am going to ask that this thread sticky status is removed so I can re post it without your opinions, perceptions and practices that are not based on factual and provable phenomena. Please resist the temptation to post your opinions, perceptions and experiences in stickiied threads in future. Thanks for your co-operation.

 

[Victory Pete]

VP we are not dealing with your opinions, perceptions and practices here.

This thread was the result of a request made directly to me to provide some factual concise and accurate information on the subject of how to best tune your guitar to avoid common issues that are commonly experienced by many guitar players.

I am going to ask that this thread sticky status is removed so I can re post it without your opinions, perceptions and practices that are not based on factual and provable phenomena. Please resist the temptation to post your opinions, perceptions and experiences in stickiied threads in future. Thanks for your co-operation.

So why do we have Forums? I didnt know my math was not "factual consise and accurate information". Such as 2 to the 1/12 power.
VP

 

[TelePaul]

Nice one Mutt! But do we HAVE to use our ears? How useful is a tuner in this situation? I mean I understand that you're tuning notes relative to each other but isn't there some technology that'll do this for me?

 

[muttley600]

Nice one Mutt! But do we HAVE to use our ears? How useful is a tuner in this situation? I mean I understand that you're tuning notes relative to each other but isn't there some technology that'll do this for me?

In one sense it's all down to what's good for you and your own acceptable tolerances. For some just using a tuner to tune each string to eadgbe is fine and that's good. The info I posted above is aimed at those that want to understand why it can appear that their guitars are never quite as "in tune" as they would like.

For me When I'm at home or recording I'll definitely tune up as I described. When I'm in a live situation I might start that way but owing to the nature of live performing and the volume levels that brings I'll often just use a tuner to get the thing as close as I can.

As far as technology to help. I guess you could get a tuner that has a memorey and program in the best tempered tuning for each guitar you use. For me I think just persisting with the method and getting used to it is the way to go. Once you get in the habit it isn't that hard to do. Definitely worth it for home practice and I think essential for recording. Ultimately it's down to what you find acceptable though.

 

[muttley600]

So why do we have Forums? I didnt know my math was not "factual consise and accurate information". Such as 2 to the 1/12 power.
VP

VP, I haven't said your maths is either correct or incorrect. If you recall I actually asked if you could post your calculations so I could make that judgement.

As for "2 to the 1/12" or 12th root of two as it is more commonly expressed, I was pointing out that it isn't "the ratio for equal temperament" as you stated but a method of calculating fret spacings on a stringed instrument and applicable to 12 note equal temperament. Equal temperament does not have "a ratio" of it's own. There are many. Does that make sense to you now?

All I am attempting to do is keep the information posted in this thread as accurate and accessible as possible. I have only asked you to clarify a few things and pointed out some ambiguities in your post. If you find that confusing or offensive then I don't really know what to add. If you have a grasp of the subject material in such a way that you can add or expand on what I posted initially I would be happy to hear it. I'm afraid I didn't find your post that easy to understand and simply asked for you to clarify it. If you do have a good grasp of the subject that should be a fairly easy task. Yes? No?

Anyway you can respond or not as you choose in this thread now as I have had the sticky status removed and re posted the info in another locked thread for now. I look forward to you clearing up these misunderstandings so we can push the subject in a positive direction for everyone's benefit.

 

[Victory Pete]

VP, I haven't said your maths is either correct or incorrect. If you recall I actually asked if you could post your calculations so I could make that judgement.

As for "2 to the 1/12" or 12th root of two as it is more commonly expressed, I was pointing out that it isn't "the ratio for equal temperament" as you stated but a method of calculating fret spacings on a stringed instrument and applicable to 12 note equal temperament. Equal temperament does not have "a ratio" of it's own. There are many. Does that make sense to you now?

All I am attempting to do is keep the information posted in this thread as accurate and accessible as possible. I have only asked you to clarify a few things and pointed out some ambiguities in your post. If you find that confusing or offensive then I don't really know what to add. If you have a grasp of the subject material in such a way that you can add or expand on what I posted initially I would be happy to hear it. I'm afraid I didn't find your post that easy to understand and simply asked for you to clarify it. If you do have a good grasp of the subject that should be a fairly easy task. Yes? No?

Anyway you can respond or not as you choose in this thread now as I have had the sticky status removed and re posted the info in another locked thread for now. I look forward to you clearing up these misunderstandings so we can push the subject in a positive direction for everyone's benefit.

The ratio 2 to the 1/12 power is the ratio for 12 interval equal temperament, which is of course the most popular and the one used in most electronic tuners.
VP

 

[muttley600]

The ratio 2 to the 1/12 power is the ratio for 12 interval equal temperament,
VP

That is not what you said to start with, but is more or less what I said so thanks for that.

which is of course the most popular and the one used in most electronic tuners.

Just so I can be clear on this, are you therefore saying that using an electronic tuner to tune each individual string will put your guitar in 12ET and the problem of inaccurate intervals occurring is overcome?

 

[Victory Pete]

That is not what you said to start with, but is more or less what I said so thanks for that.

Just so I can be clear on this, are you therefore saying that using an electronic tuner to tune each individual string will put your guitar in 12ET and the problem of inaccurate intervals occurring is overcome?

That is what I said, I have been using only the 12ET, as most others have been also by way of the electronic tuners. What other ET is there that is so widespread and popular? Using an accurate tuner for each individual string will put your guitar in ET, no it will not overcome the limitations and inaccuracies of ET. I find the major third to be the most noticable tuning compromise with ET. For example the F# in a D major chord can be improved by tuning by ear, but then other chords will be out. I have known for 20 years that ET is an acceptable compromise so one can play equally well in all 12 keys. I absolutely understand this whole concept, you just like to try to second guess me.
VP
PS "Revivise" is spelled incorrectly, it is spelled "revise"

 

[muttley600]

That is what I said, I have been using only the 12ET, as most others have been also by way of the electronic tuners. What other ET is there that is so widespread and popular? Using an accurate tuner for each individual string will put your guitar in ET, no it will not overcome the limitations and inaccuracies of ET. I find the major third to be the most noticable tuning compromise with ET. For example the F# in a D major chord can be improved by tuning by ear, but then other chords will be out. I have known for 20 years that ET is an acceptable compromise so one can play equally well in all 12 keys. I absolutely understand this whole concept, you just like to try to second guess me.
VP

No I'm not trying to second guess you. As I keep saying I am attempting to understand what it is you are trying to add to the subject. It is clear to me know that we are at cross purposes. You haven't really read and understood what I posted in my first post. The method I describe is aimed at those that find the compromises of tuning as you describe unacceptable. Can you at least please read the links in that post if you are unable to take me at my word. One of the problems is that inherent errors higher up the fingerboard are not tempered tuning to a tuner across the board. Learning to temper the tuning yourself helps with this. If it's not for you thats fine.

Now that we have cleared up one of your points lets move on to another. Your reference to the circle of fifths? How does this relate to the debate? Leave aside your calculations for now if you can't lay your hands on them thats OK. Lets focus on how it adds or explains what is being discussed here.

What other ET is there that is so widespread and popular?

There is a wealth of both electronic composition and also other more mainstream composition focusing on both 16ET and 31ET. If you like I can point you to some of it. I myself have built and fretted instruments to play in 31ET. The intervals in 31ET are strikingly better in nearly all cases.

 

[muttley600]

PS "Revivise" is spelled incorrectly, it is spelled "revise"

Yes I know I have asked a mod to correct the typo already. Thanks for pointing it out though. I'll be sure to do the same in your posts as typos occur. Start with this one.

It is frustrating to have just set up and perfectly tune and intonate a guitar to have the owner immediately start messing with the machine heads. It is equally frustrating to try to explain Equal Temperment to those people who are so stubbornly proud of their "Golden Ears". In my recording studio I insist everyone use my Peterson V-Sam Tuner, there is always someone who tunes by ear or will start messing with the tuning after we start the session. I hope Equal Temperment will become more of a topic in the future.
20 years ago I was confused by the science of tuning and stummbled on Equal Temperment in an Encyclopedia (remember those?) I didnt want to accept that music was not so exact and pure, but I got the message. I attempted to see what would happen if a plotted the "Circle Of Fifths" in a chart. I took an arbitrary value of 100 to start. multipied that by 3. I then divided by 2 to get 150 and plotted that value in its proper place in the 12 note interval I was plotting. I then multiplied 150 by 3 and then divided by 2 and plotted that value. (I would have to divide by 2 more than once to ensure my final value would end up between 100 and 200) I did this until all 12 spaces where full. I then compared the ratio of any 2 intervals. There were 2 ratios that repeated. I forgot exactly what they were, I have the whole experiment written down someplace. The most interesting part of all this was that I recognised a pattern of the 2 different ratios, It was the same pattern as the black and white keys of the piano, which is of course the Major Scale. I felt relieved that there seemed to be some order to this after all. This system is called "Just Intonation". The problem is you are stuck to play in the one key. Equal Temperment takes an "average" of these 2 ratios and makes one repeated interval. The ratio of Equal Temperment is 2 to the exponent 1/12 or 1.059463094. If you are curious you can take any number and multiply it by this ratio 12 times and you will end up with exactly an octave of your original number. A guitar tuned to 12ET with an accurate tuner is pure bliss!
VP

 

[Victory Pete]

No I'm not trying to second guess you. As I keep saying I am attempting to understand what it is you are trying to add to the subject. It is clear to me know that we are at cross purposes. You haven't really read and understood what I posted in my first post. The method I describe is aimed at those that find the compromises of tuning as you describe unacceptable. Can you at least please read the links in that post if you are unable to take me at my word.

Now that we have cleared up one of your points lets move on to another. Your reference to the circle of fifths? How does this relate to the debate? Leave aside your calculations for now if you can't lay your hands on them thats OK. Lets focus on how it adds or explains what is being discussed here.



There is a wealth of both electronic composition and also other more mainstream composition focusing on both 16ET and 31ET. If you like I can point you to some of it. I myself have built and fretted instruments to play in 31ET. The intervals in 31ET are strikingly better in nearly all cases.

I understand your original post, I have tempered tuning in my Peterson, I have tried them and for me I prefer ET with its inherent flaws. It is repeatable and dependable, which is important in a recording studio where a year or more later the instruments will all be in tune.
My experiment with the Circle Of Fifths was an interesting experiment involving the 2 ratios I discovered in my chart. The 2 resulting ratios displayed 2 familiar patterns, the Diatonic Major Scale and the Pentatonic Natural Minor Scale. Food for thought.
I have yet to walk in to a Guitar Center or any other store and see a guitar with 16 or 31 frets to the octave, I would love to try one.
ViP

 

[muttley600]

I understand your original post, I have tempered tuning in my Peterson, I have tried them and for me I prefer ET with its inherent flaws. It is repeatable and dependable, which is important in a recording studio where a year or more later the instruments will all be in tune.

That's absolutely fine and understandable but as I started by pointing out originally this thread is designed for those that want a concise and understandable explanation of why we are at where we are at today and also those that want to develop their ear and understanding of the reasons behind modern tuning systems. Simply saying use a tuner does none of those things. If thats your preferred option then fine but it isn't really relevant to the subject.

My experiment with the Circle Of Fifths was an interesting experiment involving the 2 ratios I discovered in my chart. The 2 resulting ratios displayed 2 familiar patterns, the Diatonic Major Scale and the Pentatonic Natural Minor Scale. Food for thought.

Not really I'm still unclear as to how it relates to the subject and without a more detailed explanation I can see how it is of benefit. The only real need to bring up the subject of the circle of fifths in relation to this topic is to demonstrate how resolving the octave using pure fifths leaves us with what is known as the Pythagorean comma. It is that comma that is used to show that the ratios of pure intervals can never be adequately resolved and gives us an explanation for the value by which each interval must be tempered to achieve our goal. I shall explain that in a future post in the new sticky thread. If your exercise demonstrates something else to do with this subject I'd be glad to investigate it, That's why I asked to see it in detail. I can't see how it does and it definitely doesn't relate to any just intonation system as you claim. At least not as far as I can see but I intend to cover just intonation in another post later so if you could explain that as well I could include your observations on that too..

I have yet to walk in to a Guitar Center or any other store and see a guitar with 16 or 31 frets to the octave, I would love to try one.
ViP

Your not likely to see them in a guitar centre. The instruments I built were not guitars but I remember seeing a 34et guitar done by Larry Hanson if I remember correctly. The most common ET outside of 12 note are 16, 31 and 34. Get too far above that and it gets impossible to both fret and play accurately.

 

[Victory Pete]

That's absolutely fine and understandable but as I started by pointing out originally this thread is designed for those that want a concise and understandable explanation of why we are at where we are at today and also those that want to develop their ear and understanding of the reasons behind modern tuning systems. Simply saying use a tuner does none of those things. If thats your preferred option then fine but it isn't really relevant to the subject.


Not really I'm still unclear as to how it relates to the subject and without a more detailed explanation I can see how it is of benefit. The only real need to bring up the subject of the circle of fifths in relation to this topic is to demonstrate how resolving the octave using pure fifths leaves us with what is known as the Pythagorean comma. It is that comma that is used to show that the ratios of pure intervals can never be adequately resolved and gives us an explanation for the value by which each interval must be tempered to achieve our goal. I shall explain that in a future post in the new sticky thread. If your exercise demonstrates something else to do with this subject I'd be glad to investigate it, That's why I asked to see it in detail. I can't see how it does and it definitely doesn't relate to any just intonation system as you claim. At least not as far as I can see but I intend to cover just intonation in another post later so if you could explain that as well I could include your observations on that too..
Your not likely to see them in a guitar centre. The instruments I built were not guitars but I remember seeing a 34et guitar done by Larry Hanson if I remember correctly. The most common ET outside of 12 note are 16, 31 and 34. Get too far above that and it gets impossible to both fret and play accurately.

My experiment is quite relevant as it dwells in the mathematical science of vibrations, scales, intervals and the reasons we have discrepancies in our tuning system. It has inspired me to continue my ongoing research of the science of music.
VP

 

[muttley600]

My experiment is quite relevant as it dwells in the mathematical science of vibrations, scales, intervals and the reasons we have discrepancies in our tuning system. It has inspired me to continue my ongoing research of the science of music.
VP

VP, that very well may be the case but can you understand that in the way you have explained it here we are unable to access that relevance. All I'm asking is that you explain it. I'm genuinely interested from the point of view of both a musical acoustics lecturer and a luthier. Please share it with us and then we can include it in the stickied thread. Thanks.

 

[Victory Pete]

VP, that very well may be the case but can you understand that in the way you have explained it here we are unable to access that relevance. All I'm asking is that you explain it. I'm genuinely interested from the point of view of both a musical acoustics lecturer and a luthier. Please share it with us and then we can include it in the stickied thread. Thanks.

If I cant readily find my original papers, I may redo the chart and post a picture of it. I am still interested in the outcome I achieved 20 years ago. I have always been interested in math and patterns. I always try to find some order in everything I do, I guess it is the scientist in me.
VP

 

[tdukex]

muttley, thanks for doing this. It is appreciated. The closed sticky is a good idea.