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Sep 2, 2019 - 6:25:46 PM

2718 posts since 10/17/2009

quote:
Originally posted by BrooksMT


The dissonance between 1st and 2nd string, while playing the 1st position G chord in DoubleC tuning, can be alleviated by adjusting the tension of the 1st string. Of course, this will make other frets play off pitch...

The problem with the chord is not about equal temperament. But as you mentioned it a few times... 

The chord is gDGdd. Contains fifth, octaves and unisons. (no third).   There should be be no dissonance between the 1st and 2nd string, it's a unison; and makes an octave for the 4th string (2nd fret). An instrument frets set up to ET will achieve that. The Ds are fifth of the G; but narrow by a mere 2 cents.

That 2 cents makes that d about .35 hz flat. The cps difference in (beating) is slow, slower than typical vibrato. Vast majority folks, small 2 cent difference would not be particularly noticeable; esp in context of acoustic envelope of stuck string instruments (as opposed to bowed, wind or electronic oscillation); and in context of the actual music played Even few where might be noticed, not considered "dissonant". 

Flattening the 1st string more will not get make the G/d closer to pure 3/2 fifth; but rather make it worse. 

Edited by - banjoak on 09/02/2019 18:27:16

Sep 2, 2019 - 10:01:59 PM

844 posts since 8/7/2017

banjoak

My suggested flattening of the 1st string was not to make the chord sweeter, but to reduce dissonance in the desired unison of 1st and 2nd string. I hear that in one of my banjos when tuned to doubleC when making the G chord 1st position, and assumed that was the problem. If I assumed wrong, then my advice would be wrong, of course.

This banjo has interesting tonal characteristics, which after 3 years of play I am still discovering. For instance, the bridge needs to be angled opposite to the angle I see on other banjos (ie mine is angled so that the 4th string is shorter than the 1st string). It came that way from the seller, who is a very experienced banjoist. And my exploration of harmonics shows he knew what he was doing :-)

Bridge position is important to get good harmonics, if you have the ears to discern good from bad harmonics. I will even adjust position when tuning to a different key. We are getting into the realm of non-linear responses at high orders of harmonics, and I think theory gets shaky in that realm. So ears are the best way to go...if it sounds good to you, then that's what you should follow.

Sep 3, 2019 - 10:31:11 PM

2718 posts since 10/17/2009

quote:
Originally posted by BrooksMT

banjoak

My suggested flattening of the 1st string was not to make the chord sweeter, but to reduce dissonance in the desired unison of 1st and 2nd string. I hear that in one of my banjos when tuned to doubleC when making the G chord 1st position, and assumed that was the problem. If I assumed wrong, then my advice would be wrong, of course.
 



You seem to miss the point. Tune the open 1st string to match the 2nd string 2nd fret will make a perfect unison. (no matter the ET, JI or other)

But that the fretted banjo is highly likely designed that the 2nd fret is ET 200 cents above the open string. Tune the open 1st string to same 200 cents above. It has no cent difference in the unison; defines lack of dissonance. (perfect unisons are easy to hear)

If C=264Hz; the 200 cent D=296.3Hz

Similar the 4th string 2nd fret D should make a perfect octave. (148.15Hz); also lack of dissonance. (perfect octaves are easy to hear). 

The suggestion to flatten the 1st string; will be < 200 cents, would not make a unison, achieve less dissonance in the D notes.

The OP did not indicate the D notes sounded that out-of-tune dissonant; (likely used a electronic tuner that put all the D notes at 200 cents)... as mentioned probably rather the opposite... just too much D resonance. 

 

quote:
 

Bridge position is important to get good harmonics, if you have the ears to discern good from bad harmonics. I will even adjust position when tuning to a different key. We are getting into the realm of non-linear responses at high orders of harmonics, and I think theory gets shaky in that realm. So ears are the best way to go...if it sounds good to you, then that's what you should follow.


The bridge position on a given fretted instrument - is about getting the frets to play in-tune as designed. Design of 12T fretboard is the 12th fret matches the 1st overtone.  If instrument is fretted and set-up properly, all the frets intonation should be right. Bridge compensation in angle, or offset in bridge; has to do with adjustments due to differences in string properties; gauge/mass/tension/end stiffness and clearance; again goal simply to match the fret layout.

Non-linear responses of high order harmonics? On a banjo, rather moot, not going nor accomplish much, nor way to really address issue. More important, it's pointless if it makes the frets fundamentals so they don't play in tune.

On a 12TET fretboard; simply changing placement/angling of the bridge wil take it out of ET, but won't change to be JI or likely any very useable good sounding intonation. (unless like some limited or funky out-of-tune sound).

I agree with use your ears. In context of the whole; all the notes, and in playing actual music. Keep in mind, if playing for or with others; might not be impressed by supposed improvements. (making 2 frets sound better at the expense of 10 others; including unisons, octaves, fifths; sounding worse?)

Edited by - banjoak on 09/03/2019 22:46:30

Sep 4, 2019 - 2:01:03 AM

2718 posts since 10/17/2009

quote:
Originally posted by wooster

On the subject of temperament I came across this video which I found to be quite a striking example of the differences made by the two. I don't know if this is of interest to anyone or not but I found it really interesting to listen to the contrasts

youtube.com/watch?v=Yqa2Hbb_eIs


This is a bit drift from the OP issue, probably should be in Music Theory. But to address some points...

That video initially (up to 1:16) demonstrates the difference in the sound of C chord, ET vs JI... as noticed on a held sustained organ chord.

The rest of the video showing the bad C# chord is a bit wrong for really demonstrating Just Intonation; (and typical issues). The keyboard is in something Yamaha calls "Pure Temperament", not exactly 5-limit  JI. While the diatonic scale is 5-limit Just; it rather sets some chromatic notes a bit different; for a reason. PT exaggerates dissonance, (ironically, normal JI for C major, make a good C# major chord; but has little use in key of C). A more relevant issue to show of single diatonic JI would have been the D chord, major or minor; and 680 cent fifth. (the Yamaha doesn't fix)

I think there is an error in the organ's computation of the "Pure Tempered" 3rd note in C#major chord. The chord sounds fine until he presses the 3rd note organ key, which is too flat for the chord.

The third in c#/f/g# actually about 428 cents; about 42 cents too sharp (fifth is right).  But, it is not an error... that specific tuning wasn't designed entirely JI, nor to make a good C# chord (on key of C major setting). Rather seems to be designed to achieve some other useable, non-diatonic chords sound good; such as III - E major, or VI - A major.

But my table of Just Intonation (discussed in the thread I cited earlier) shows that the JI 3rd note should be 15 cents sharper than the ET note. In other words, my table would not produce a note that's too flat for the chord....which is what I experienced with my banjo

The JI major third of a chord should be 14 cents flatter than an ET. The PT achieves that 386 cent third for diatonic scale, and main chords (C# maj is not part of)... it will retains those relationships "if" simply using the transpose key (like moving capo  up). 

But, might be missing the point though; it isn't a big deal to set frets or keys on a fixed pitch instrument to play within ONE single diatonic frame in a limited way. Nor to transpose via button. The question is how to make a single fixed pitch instrument, pragmatically play all good diatonic chords; as well extend outside the diatonic; as well play in other keys?

The Yamaha has separate major and minor setting; makes for 24 different intonation layouts. Fretted instruments with JI fretboard, can't transpose via simply hit a button; and capo would not actually work; frets actually have to be moved.

Edited by - banjoak on 09/04/2019 02:08:59

Sep 13, 2019 - 3:10:56 AM

MHMR

Philippines

9 posts since 9/8/2019

I am a novice but I decided to spend the last 6 months in double c. I didn't know the chord pattens so what I did was figure out the 1-3-5 notes of the major chords. Then found the pattern for 1 on the first string, on the second and the third. After that I added the minors and now learning pentatonic scales. Its been pretty fun.

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