Equal Temperament, Meantone and Just Intonation on McSpadden

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Equal Temperament, Meantone and Just Intonation on McSpadden

Postby Robin the Busker » Tue Apr 28, 2015 2:34 am



Here is a video explaining 3 possible fret temperaments for mountain dulcimer.

And here are a couple of sound samples: The first in just intonation played noter drone in 1-5-5 and the second in quarter comma meantone played in 1-5-8 chord melody. I figure that everybody knows how equal temperament sounds!



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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby danc9 » Tue Apr 28, 2015 6:43 am

Spot on Robin!


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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby folkfan » Tue Apr 28, 2015 10:04 am

A very interesting explanation. Clear and effective demonstration of the differences in the temperaments.
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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby KenH » Tue Apr 28, 2015 6:57 pm

Good job!
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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby jcrdulci » Tue Apr 28, 2015 8:41 pm

Beautiful job of explaining everything here!! This is the clearest explanation of these three important tuning systems ever!! Thanks for doing this and thanks to Jim Woods for the great dulcimers!!!
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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby asterhunter » Wed Apr 29, 2015 6:12 am

That is excellent. I don't find one tuning "better" than the other, both have their own characteristics that are pleasing to my ear. One type of tuning might be a better choice for some types or styles of tunes however.

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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby Robin the Busker » Wed Apr 29, 2015 11:56 am

Thank you for all your comments. I've had the chance to quickly record a few more examples of different tunings in just intonation. The first clip is in D,d,d bagpipe tuning - initially played in the key of G (Ionian) and then switching to the key of D (mixolidian).



The second clip is in DdGd tuning:

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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby Stephen Seifert » Sat May 02, 2015 3:36 pm

This is just fantastic! Than you, Robin, for posting.

This video really helped me understand what the natural ear likes to hear by showing what fretless string players often do:



Unaccompanied choirs do this same kind of thing. I've been changing the tuning system in Apple's Logic X Pro to Hermode tuning in Project Settings to hear pure intervals on every chord in the key when I'm playing a keyboard. Hermode simulates how string orchestras and choirs function by analyzing the current chord and adjusting the intervals accordingly.

I would very much like to have a 155 dulcimer minus the six-and-a-half fret fretted just tuning or quarter comma mean tone. When I play fretless dulcimers, banjos, fiddle, etc., I make the adjustments.

Don Pedi plays a lot with Old-Time fiddler Bruce Greene. Old-Time fiddlers, to my ears, are closer to Just Tuning than our equal-tempered dulcimers. I would love to hear Don use one of your dulcimers as he jams with Bruce. I suspect there would be a subtle sweetness I would very much enjoy hearing and feeling.

Robin, if you could just have one of those instruments for noter-drone playing, which would it be?

Thanks again for doing this. So great hearing your just dulcimer alongside the Homer Ledford.
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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby Robin the Busker » Sat May 02, 2015 8:19 pm

Thank you for your post Stephen.

I watched that violin intonation lesson a while back when I first became interested in early dulcimer fretting patterns - as you say, it provides a wonderful insight into how intonation can vary and is always a compromise of sorts.

I fretted a McSpadden dulcimer with staple frets purely by ear last year (no measurements, tuner or reference notes) and ended up with just intonation. It was that experience that put me on to how Homer Ledford had produced his scale by using two strings set at a perfect 5th and then placing the frets for the least dissonance with the bass string root note. It took me a while to work out the math behind just intonation using Ptolemy's intense diatonic scale fractions but, with the help of Bob Reinsel, I now have an excel fret calculator, which I sent to Jim Woods to make the just intonation McSpadden teardrop. It was quite a revelation to find out how well Homer's scale matched Ptolemy's calculations and my 'by ear' fretted dulcimer.

Jim Woods had previously built some meantone dulcimers and had told me he had a spare fretboard in meantone that I may be interested in, so I asked him to build an instrument around that, which gave me the chance to do some side by side comparisons.

Regarding which temperament I like best for noter drone playing - Well, that's a hard one to answer as feel I need some more time exploring each system. What I can say is that equal temperament is my least favourite (not that it is 'bad' at all, but I do notice the sharp 3rds and non perfect 5ths particularly). Meantone is a little difficult to tune initially as I find that I do need to compromise the open string tunings a little in order to get the best from the scale. This is because the 4ths and 5ths are not perfect. On the other hand, just intonation is spot on - and it is lovely to have a dulcimer where you can tune the bass, middle and melody strings to a perfect 5th and still have the 3rd fret as a perfect octave of the bass string. I like the natural blend of notes in just intonation although the 6th is an acquired taste. It is in the position of least dissonance with the root note bass string but can be hard to justify against the perfect 5th middle drone within some music passages but not others - however, I can always pull the note a little sharper with my noter if the phrase requires Pythagorean intonation of the 6th. Of the 3 temperaments I reviewed here I would pick just intonation as my favourite for noter drone playing simply because of its lovely blends - it is a joy to play!

I have a good number of old dulicmers (Ledford, Presnell, Glen, Tignor, Amburgy, Wilson, Neuhauser, Jeffreys,) none of which are in equal temperament. The slightly flattened 3rd and flattened 6th seems to be a common feature but, bar the Ledford, none is completely in just intonation (nor any other strict intonation system I can find). I think that the Clifford Glen I have probably has the nicest intonation of my old dulcimers (although it is not perfect).

I remember you putting up a thread a few years ago Stephen where you talked about how good some old dulcimers sounded in Ionian but not in other modes. What I have found is that dorian is quite a problem on any dulcimer in or close to just intonation for the Ionian scale.. But, for some reason, Aeolian is lovely on a dulcimer set for Ionian just intonation. I wonder if this is because Aeolian is centred on the 6th of the scale (the relative minor)?
Here is a short clip of my just intonated McSpadden in Aeolian mode:
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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby dholeton » Mon Oct 05, 2015 11:37 am

Robin
Thanks for the excellent explanation on the temperaments. I remember somebody in the 1980's checking the fret spacing on my dulcimer with equal temperament spacing and saying something like "yep, the frets are correct for this dulcimer". Even with "correct" fret spacing, it still wasn't unusual to enter a room full of people getting ready to play music and somebody would say "Oh, you brought one of those?"

This comment in your last post has me wondering.

What I have found is that dorian is quite a problem on any dulcimer in or close to just intonation for the Ionian scale.. But, for some reason, Aeolian is lovely on a dulcimer set for Ionian just intonation.


If the Aeolian with just temperament that sounds lovely is in DAC tuning, do you think Dorian tunes in DAC tuning with carefully (just temperament) placed 6.5 and 13.5 frets would sound good too? There are some Dorian tunes that can start and end on the 1st fret and use the 6.5 fret (like Arran Boat Song, Road to Lisdoonvarna, and Scarborough Faire). At times I play Dorian tunes in DAC tuning, so I'm thinking a 6.5 just temperament fret should make Dorian tunes as lovely as Aeolian tunes in just temperament.

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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby Robin the Busker » Tue Oct 06, 2015 10:23 am

Hi Dave,

The problem lays in the fret spacing of the 4th fret (2nd of the scale). In just intonation the 2nd of the scale is 4 cents sharp of equal temperament - this is where the dorian scale starts. However, the 1st fret (6th of the scale) is 10 cents flat of equal temperament - and this is where the Aeolian scale starts.

We tend think about the modes in terms of equal temperament, with each mode staring from a different fret. But it is just not as simple as that. Modes have their own intonation that is not directly related to just a start point on the Ionian scale. However, some modes do fit the just intonated Ionian scale. Aeolian, as the relative minor of the scale, is one that 'fits' because the 5th is perfect. Whereas Dorian sounds awful due to wolf notes - a wolf 5th in particular.

In answer to your question about a carefully placed 6.5 giving dorian from DAc on a just intonated fretboard. Well it is yes and no. Yes, it could give a usable dorian scale but 'no' as that 6+ will not give an Ionian scale from the nut (the 1st fret is about 15 cents out from giving an accurate 2nd of the scale).

All in all - if a dulcimer has its frets set by ear then the scale will err towards just intonation as it is easier to set frets that are 'in tune' than ones that are all 'slightly out' like equal temperament. However, such a dulcimer (99% of pre-revival dulcimers!) will struggle to sound 'good' when moved away from the tuning, string gauges and set-up that the maker used to set the frets.
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Re: Equal Temperament, Meantone and Just Intonation on McSpa

Postby dholeton » Thu Oct 08, 2015 10:12 am

Thanks Robin
That said, I think it would be a surprise to discover one of the old dulcimers with frets arranged for Dorian mode with Just Intonation.
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