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#3164217 10/15/21 11:07 AM
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Can anyone give instructions for tuning 1/6 comma meantone? Thanks smile

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Hi Hombre,

It really helps to some background study on this topic to get a basic orientation to the concept of meantone style tuning.

First is to grasp what a comma actually is: I think a practical way to explore the comma is to tune a series of 4 perfect 5ths. If you started on middle C, I would tune the following basic pattern.

Tune up a 5th, up another fifth and then down a pure octave. Up a fifth, up a fifth and down and octave.

C4-G4, G4-D5, D5-D4, D4-A4, A4-E5, E5-E4

Tune everything as pure as you can and then see what the resultant C4-E4 third sounds like. If you are doing things correctly it will be a pythagorian 3rd and its *very* edgy and fairly dissonant.

Then, play around with flattening the fifths in the sequence until you are able to get the resultant C4-E4 third pure. Then you can try for some pleasant middle ground: That will put you in the realm of 1/6 comma style.


Ryan Sowers,
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Ok, does octave "size" matter? (c.f. https://www.billbremmer.com/wp-content/uploads/2019/02/octave_types.pdf)

Anyway, am I understanding right that 1/4 meantone means that most thirds are pure, and 1/6 is this compromise between pure thirds and fifths?

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1/4 meantone has eight pure Major thirds and the fifths are all quite narrow (-5.38 cents vs. -1.96 in equal temperament) Except for the "Wolf" (D# to G#) which is 35.7 cents wide. The four remaining thirds are all super-wide (41 cents wide, vs. ET thirds of 13.7 cents)

1/6 meantone has eight moderately wide thirds (7.2 cents vs 13.7 in equal temperament) and the fifths are better (-3.6 cents) and the wolf is only 16 cents. The four remaining thirds are 26.7 cents wide.

In each case, the fifths are all going to sound worse than in ET. You're sacrificing them for those 8 slower (purer) thirds.

I have zero experience tuning this aurally, but if I were to approach it bluntly, I'd tune around the circle of fifths both ways, starting from A (La), making each fifth and fourth sound twice as bad as it does in equal temperament. So I'd shoot for maybe 2 beats per second for my fourths, and maybe a beat per second with my fifths. When you get to D# and G#, stop, and don't tune that fifth. That's your wolf interval.

Or I'd download any number of free tuning apps that come pre-loaded with temperaments. "Pano Tuner" (not a typo) is one popular free app.


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Here are instructions for 1/6th-comma meantone tuning:
https://musintra.sitehost.iu.edu/de...raments/1-6-comma-modified-meantone.html

I've used their 1/8th-comma tuning and it does well for Classical and early Romantic piano works. Not Chopin -- he modulates all over the place.

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Anthony's instructions are very practical. (Hi Anthony!)

I'd recommend an aural approach, because learning to listen is at least half the fun and it will be much more rewarding. You'll also gain a more intuitive approach to what compromises must be made when tuning a piano.


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I suspect 1/4 comma meantone is much easier to tune. A 17th is two octaves and a major 3rd. In 1/4 comma meantone, two octaves and a just 3rd are used to generate a 17th. A 17th also results from concatenating 4 ascending 5ths. Once you have the 17th as two octaves and a just 3rd, you construct the 4 ascending 5ths to be each of the same relative intervals and land on the 17th that was constructed by two octaves and a just 3rd. These 1/4 comma 5ths will be slightly diminished from just 5th.

You then fill in by descending octaves. If you started on C4, you now have C4, D4, E4, G4, A4. You then can repeat the process starting on other notes that already have to fill in the full temperament, and then tune octaves from that.

If you get proficient at setting the 1/4 comma 5ths directly, you can stack 4 of them and confirm you have two octaves and a just 3rd.

There may be better methods, but that's how I tuned the clavichord I once owned.

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I wonder why anyone would want to tune the modern piano in 1/6 Comma Meantone? While I agree with Ryan Sowers that aural tuning skills are important, there is not a really good and reliable way to accurately tune a 1/6 Comma Meantone Temperament. Any of the Meantone temperaments are defined as having all 5ths tempered by the same amount. The fraction that is always noted such as 1/4, 1/5, 1/6, 1/7, etc., is a fraction of the syntonic comma which is the difference between the very wide, so-called Pythagorean Major 3rd and a pure third: 21.5 cents. If you divide that by 11, each 3rd will effectively be 2 cents narrow and they will all agree, not leaving the one, un-tuned, so-called "wolf" 5th. In other words, Equal Temperament is the equivalent of a 1/11 Comma Meantone Temperament.

The 1/6 Comma Meantone has -3.6 5ths. Almost twice as much as ET 5ths. I suppose you could guess at them by ear but there is a far simpler and very accurate way of programming an ETD to do it. The Sanderson, Tunelab, Reyburn and Verituner all have "Temperament" functions in them. They may already have a 1/6 Comma Meantone in there. If not, just select a Temperament page and label it "1/6 Comma Meantone" and enter the following Data:

C: 4.8
C#: -6.4
D: 1.6
D#: 11.2
E: -1.6
F: 8.0
F#: -4.8
G: 3.2
G#: -8.0
A: 0.0
A#: 9.6
B: -3.2

Then, take the inharmonicity samples, the same as when tuning Equal Temperament and apply the "Temperament" page data. The result will be a properly calculated 1/6 Comma Meantone Temperament for that piano.


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The following method for tuning 1/6 meantone requires being proficient at hearing the beats to set thirds, fourths, and fifths in the temperament:

https://musintra.sitehost.iu.edu/de...raments/1-6-comma-modified-meantone.html

I doubt that there is a more straightforward process, as Bill noted in the previous posting.

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Thanks everyone! Just curious to try some classical music this way on the piano.


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