Guitar tuning and temperament.
- Thread starter muttley600
- Start date
miroslav
Cosmic Cowboy
I just use a Peterson VSAM virtual strobe tuner....though one thing, I never tune to the open strings, rather I always tune to fretted strings, and I do that at the 7th fret since it's the reative midpoint of the neck for most chord playing.
I find that tuning to open strings only works well if you spend most of your time playing in the first position and using lots of open chords.
But for Barre chords and leads (which is about 90% of my playing)...when you fret a string it will always go sharp relative to the open string...so I tune 'em fretted since that's how I play them most of the time.
That way...the fretted notes are the ones in tune with other instruments using the 440 Hz reference (or whatever you prefer).
That said…the enduring problem when tuning (open or fretted) is always the G string. It needs to be a pinch flat for most Barre chords, but in-tune for leads. What I do, is set it in-between…and then I just avoid fretting the G too hard when playing chords, but for leads I can "work it" into tune as I play.
Most days I can find an acceptable “fudge”.
I find that tuning to open strings only works well if you spend most of your time playing in the first position and using lots of open chords.
But for Barre chords and leads (which is about 90% of my playing)...when you fret a string it will always go sharp relative to the open string...so I tune 'em fretted since that's how I play them most of the time.
That way...the fretted notes are the ones in tune with other instruments using the 440 Hz reference (or whatever you prefer).
That said…the enduring problem when tuning (open or fretted) is always the G string. It needs to be a pinch flat for most Barre chords, but in-tune for leads. What I do, is set it in-between…and then I just avoid fretting the G too hard when playing chords, but for leads I can "work it" into tune as I play.
Most days I can find an acceptable “fudge”.
muttley600
Banned
Seriously I'd be interested to see what you are investigating with this whether or not it has any immediate relevance to the thread. One of the ways you get students up to to speed with the whole subject is to get them to map out and calculate the ratios of different tuning temperaments. I'm interested to see how you derive a workable temperament from your circle of fifths especially if it results in a genuine just system.
Victory Pete
Banned
Circle Of Fifths Experiment
100 .936442615
106.7871094 .94921875
112.5 .936442615
120.135498 .94921875
126.5625 .936442615
135.1524353 .94921875
142.3828125 .94921875
150 .936442615
160.1806641 .94921875
168.75 .936442615
180.2032471 .94921875
189.84375 .94921875
200
This is basically it. To obtain the 12 values I started with 100 times 3 divided by 2= 150. Then I did the same for 150. 150 times 3 divided by 2 twice, because I want my number to be between 100 and 200. I repeat this in the same order until all spaces are filled. Then I divided the numbers next to each other to obtain their ratio. I noticed 2 intervals appeared exactly the same,.94921875 and .936442615. Then I noticed that there are 2 instances that .94921875 are next to each other. It corresponds to the intervals in the Major Scale. There are only 2 intervals that have half steps in the Major Scale. I found this to be very interesting. Like it had some order. The ratio for 12ET is .943874312, the average of the 2 ratios above is .942830682. That is interesting. Apparently when I post this it does not come out like I had it when I typed it. I originally had all the columns in line. sorry for the disorder.
VP
100 .936442615
106.7871094 .94921875
112.5 .936442615
120.135498 .94921875
126.5625 .936442615
135.1524353 .94921875
142.3828125 .94921875
150 .936442615
160.1806641 .94921875
168.75 .936442615
180.2032471 .94921875
189.84375 .94921875
200
This is basically it. To obtain the 12 values I started with 100 times 3 divided by 2= 150. Then I did the same for 150. 150 times 3 divided by 2 twice, because I want my number to be between 100 and 200. I repeat this in the same order until all spaces are filled. Then I divided the numbers next to each other to obtain their ratio. I noticed 2 intervals appeared exactly the same,.94921875 and .936442615. Then I noticed that there are 2 instances that .94921875 are next to each other. It corresponds to the intervals in the Major Scale. There are only 2 intervals that have half steps in the Major Scale. I found this to be very interesting. Like it had some order. The ratio for 12ET is .943874312, the average of the 2 ratios above is .942830682. That is interesting. Apparently when I post this it does not come out like I had it when I typed it. I originally had all the columns in line. sorry for the disorder.
VP
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TelePaul
J to the R O C
This has got me thinking about 3-saddle Tele bridges. Some douche on another forum discouraged another poster from buying a 3-saddle Tele as it would never fully intonate. But if, in the majority of cases, a guitar is never fully in-tune then I suppose there's nothing a six-saddle bridge, graphite nut or locking tuners will do to change that!
DrewPeterson7
Sage of the Order
Well, there's a question of degrees. It's like the old joke - "a farmer and an engineer are standing at one side of the room. Across from them is the most beautiful girl they've ever said. They want to run up to her to be near her immediately, but she waves them off and says, 'you two have to take turns - each turn you can walk only half the remaining distance between me, but no further.' The engineer throws his arms up in frustration, and storms out saying, 'but that means we can never get to you!" The farmer watches him leave, smiles, and says, 'yeah, but I bet I could get close enough!"
Just because you can't get it 100% perfect doesn't mean it doesn't matter if you can get 90% or 98% of the way there - it matters hugely.
muttley600
Banned
VP, I am even more confused now. How is this a a circle of fifths? I cannot for the life of me fathom what you are calculating here. It must just be me but it is not at all obvious?
muttley600
Banned
You can get a three saddle tele bridge to intonate just fine. Don't sweat it.
Ultimately though you are correct, we are stuck with what we got but as Drew has pointed out it is all about understanding how and why and then getting as close as you possibly can or need to..
Victory Pete
Banned
First of all I arbitrarily chose 100hz as my tonic. I then plotted its fifth, 150. Then I plotted 150's fifth,225 but divided by 2 to fit it in my octave of 100hz to 200hz, I then proceded to go through all the fifths in the same way untill all 12 tones were in place. Do you understand that?
VP
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Victory Pete
Banned
You can get a three saddle tele bridge to intonate just fine. Don't sweat it.
Can you explain how you can get a common saddle to intonate 2 different size strings correctly? Do you mean just in the ballpark?
VP
suprstar
It aint ez being green
Hey Mutt, I told ya I get some facts together for ya.. So we were talking about 12 note scales and the amazing coincidence that ET12 frequencies line up nicely with a lot of ratios of small integers where the harmonies are, ie 1.25, 1.3333, 1.5, 1.66666, 1.8, etc..
12 is a great number for scales. In a 12 note scale, all frequency difference betw equal and just temperament are within 1%. 12 is the first number where this is true. 12 also contains more consonants than dissonants. 12 is the ONLY number where both these statements are true.
After googling around, I'm even MORE amazed at how well it all lines up mathematically.
About ET16 and ET31: The ET31 scale has all seven basic intervals to a good approximation, some with better accuracy than the twelve-tone scale, but the most important fifth (3/2) interval is less accurate than in the twelve-tone scale (2^18/31=1.495). The ET41 scale is the first with a better fifth (3/2) interval than the twelve-tone scale (2^24/41=1.5004). ET16? I see nothing remarkable about ET16 at all:
1.044 1.091 1.139 1.189 1.242 1.297 1.354 1.414 1.477 1.542 1.610 1.682 1.756 1.834 1.915 2.000
overall it looks pretty bad ??
The ET53 scale has all seven basic intervals with a better accuracy than the twelve-tone scale (the fifth is 2^31/53=1.49994). All within 0.1% actually, very nice! But do YOU want to lug around a keyboard with 53 keys per octave?
12 is a great number for scales. In a 12 note scale, all frequency difference betw equal and just temperament are within 1%. 12 is the first number where this is true. 12 also contains more consonants than dissonants. 12 is the ONLY number where both these statements are true.
After googling around, I'm even MORE amazed at how well it all lines up mathematically.
About ET16 and ET31: The ET31 scale has all seven basic intervals to a good approximation, some with better accuracy than the twelve-tone scale, but the most important fifth (3/2) interval is less accurate than in the twelve-tone scale (2^18/31=1.495). The ET41 scale is the first with a better fifth (3/2) interval than the twelve-tone scale (2^24/41=1.5004). ET16? I see nothing remarkable about ET16 at all:
1.044 1.091 1.139 1.189 1.242 1.297 1.354 1.414 1.477 1.542 1.610 1.682 1.756 1.834 1.915 2.000
overall it looks pretty bad ??
The ET53 scale has all seven basic intervals with a better accuracy than the twelve-tone scale (the fifth is 2^31/53=1.49994). All within 0.1% actually, very nice! But do YOU want to lug around a keyboard with 53 keys per octave?
muttley600
Banned
I know how to calculate a circle of fifths I'm just not getting how this is in any way new or you have come up with something that hasn't been around for hundreds of years. Am I looking for something that isn't there. You originally said this gave you a just temperament. What exactly am I looking at here? What am I expected to see other than some maths that Pythagoras had covered thousands of years ago? Interestingly you don't seem to have resolved the circle to calculate the comma which is the rub of this whole thing. It may have been easier to grasp if you separate the ratios from the assumed values and worked with a more manageable or recognisable root.
Victory Pete
Banned
All I said was I thought this was an interesting excercise. As far as the "Just" reference I made I was refering to the intervals that appear twice where at 2 points the same ratio repeats next to each other: .9492 and .9492. I said it resembles the major scale. Also the whole series of ratios certainly is anything but 12ET.
VP
muttley600
Banned
Indeed a great and happy coincidental compromise, but one composers and mathematicians for thousands of years were not willing to accept. They all pressed on looking for a system that would give them perfect intervals.
From memory it was Vicentino that originally worked in 31ET way back when. It has had a resurgence among some composers and I got asked to fret some bowed instruments for that temperament a while back. It suited at the time because quarter comma mean tone was the rage and it supposedly improved on that. I'd agree that 34et looks better. The problem with going to 34et and above is and was that around that point instruments get very very hard to handle and play especially keyborads and shorter scale fretted instruments.. 34 has been used recently and as I said earlier in the thread I remember seeing a guitar fretted for it. I wouldn't like to have to learn on it. Nightmare.
16ET is still popular among atonal composers and seems to be their weapon of choice. I don't really get why. As for 53ET I wouldn't want to to get into making instruments to play in that one. Waaayy too many keys, holes or frets.
suprstar
It aint ez being green
Got any pics or sound clips of said instrument? Just like a regular guitar with a lot more frets closer together? There's enough frets on my guitar thanks...
But that'd be a neat thing to mess around with, that's gotta be a trip!Doesn't it? I'm pretty sure electronic tuners tune you to 12ET.. You get EVEN intervals, but not 'perfect' (if you define 'perfect' as 'just'). Even is better overall, but just CAN be better if you're sticking to a single key.
muttley600
Banned
No that is not what you said. You said
"I attempted to see what would happen if a plotted the "Circle Of Fifths" in a chart."
and then you said
"This system is called Just Intonation"
I was hoping you were going to come to this conclusion yourself especially after all the coAxing I've been giving you but I guess I'll just Have to come out with it. All you have done is the calculations for a circle of fifths and wrongly labelled the resulting figures. No wonder I got confused, I was expecting something a little less Pythagorean.I'm still totally at a loss to see how this all added to the original topic but hey ho...
No you said it was just intonation it is not.
Do you mean your ratios for the calculations you did? You damn right about that. Who said they were 12ET?
Victory Pete
Banned
Here you go again with your flurry of assumptions and attacks. You seem to twist everything around to suit your own agenda. You didnt answer my question to you at post #49. My excersize is fairly simple and straight foward. Can you follow something so simple or do you purposely make everything seem complicated to boost your ego?
VP
DrewPeterson7
Sage of the Order
Post 49? I think it's clear he understands how you calculated your numbers...
I think the disagreement is that muttley disagrees with you on what they think they mean.
Victory Pete
Banned
Post 49? I think it's clear he understands how you calculated your numbers...
Are you his mindreader?
muttley600
Banned
Sadly yes I do I have both.Got any pics or sound clips of said instrument? Just like a regular guitar with a lot more frets closer together? There's enough frets on my guitar thanks...
I mentioned earlier that it wasn't a guitar but a fretted viola da gamba. I'll have to scan the pics as this was before the world went digital. Likewise the soundclips I have are pretty raw and on minidisc so I'll have to rip them. I'll do my best to get round to it.Well yes and no. You can take steps to tune a little better right across the fingerboard. Just tuning the open strings still leaves a lot of stuff to the mechanics of the strings under tension and nut hight action saddle height etc. Miroslav's post #42 is pretty much how I see it and I will still tune by ear depending on the instrument setup. It all depends what I'm trying to do at the time. Live, recording, just fiddling. I'll possibly approach all three differently.
I was just playing around with VP to try and get him to understand that much of what he states is either nonsense or bleedin' obvious. He has trouble distinguishing between the two most of the time. Like the way I have just got him to realise that his initial post in this thread was telling people he can do sums and use a tuner.