Alternate Tunings

[heyhank]

As a diatonic harp player, I have become very interested in tunings other than equal temperament. I have found some info on the subject, but it becomes very technical in a hurry. I have experimented with Just tuning on my single key harps and some different mean tone tunings on my two key harps with some success in sounding better than equal temperament tuning. Does anyone know of a good source of education on alternate tunings specifically geared toward the autoharp? I am not sure I have reached the best comprimise in tuning my instuments but will keep experimenting.

Thanks

[Bob Lewis]

I don't think one can avoid details if wanting to pass judgment on a tuning based upon reading about it. It has everything to do with math, although nothing very high level, so it might intimidate some.

The alternative is to be presented with some systems of actual tuner settings to try. There can only be a brief explanation of rationale or classification without getting back into detailed background.

My chromatics are tuned "1/6 comma meantone", which means all the fifth intervals are flatted by 3.5 cents from a perfect fifth or 1.5 cents from equal tempered fifth. For example, to tune the A-E fifth interval and calibration is A440, my tuner would say +0 for A and -2 for E, rounding the -1.5 cents to -2.

1/6 comma meantone distributes less of the syntonic comma than 1/4 comma meantone, the only true "meantone temperament". That means that 1/6 comma would have an Eb and D# 18 cents apart and both Eb chord and B7 usable instead of 42 cents apart and requiring that one tune for one or the other chord. What that in turn implies that with 1/6 I can keep a usable B7 while I have a pleasant Eb major chord. I cannot do that in full meantone, no way. I have to have one chord or the other, tune D# strings for Eb Major or for B7, avoiding or removing the other chord.

The major benefit of 1/6 comma is that diminished 7th chords are in MUCH better tuning and that the instrument is quite acceptably compatible with other instruments. No prominent note is that far off of Equal Temperament.

While 1/6 comma "meantone" flats all fifths by 3.5 cents, Silbermann is the next "sweeter" flavor at 4 cents even. I like this tuning for a diatonic to play with other instruments. I say diatonic because it doesn't have enough fifth intervals to create the conflict between Eb and B7, one string trying to be two distinctly different tunings where the circle of fifths fails to close.

A "solo tuning", either chromatic or diatonic, single key or chromatic all the same, is 2/9 comma. That uses a fifth that is 5 cents flat to a perfect fifth, 3 cents (-3) from standard (ET).

Then you have the classic meantone or 1/4 comma. That has perfect thirds but fifths which might get your attention as somewhat flat. That fifth is 5.5 cents flat.

On these temperaments that include cents in decimals, be careful with references to them, because the rounding is not always correct or acknowledged. Modern tuners like the Peterson strobe and the Turbo Tuner deal with cents in at least one decimal, so the rounding doesn't apply. For example, 1/4 comma meantone is not A at +0 and E at -4. It is actually E at -3.5. To avoid rounding errors, none of the settings is rounded until the entire series has been calculated. For example, to find a value for B, one would subtract 3.5 cents from E=-3.5, not E=-4. Thus the answer for B is -7, not -7.5 rounded to -8.

As you can see, I don't know how to talk about tuning and temperaments without getting into the numbers. The following link will lead to tunings to try. If you want to understand their origin, then we have to talk details and quite a lot of them:

Temperament Table

For more background, check out the extensive tuning resources in the links section referenced on my home page Tuning Links

[heyhank]

Thank you Bob. The links are very helpful. A little bit at a time I am actually starting to understand.

Thanks

[Bob Lewis]

I am posting as a followup to let it be known that I updated the table of temperaments linked previously and expanded the document. The link referenced in my prior post now points to a different version. The link repeated here, that document, now in better printable PDF format, is at:

Comparative Temperaments for Autoharp