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Mike Hulme

Meantone Tuning on Anglo Concertina

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4 minutes ago, Little John said:

In your case, if G minor (relative minor to Bb) is your most common key then tuning for that means centring around C

 

I guess this is what I wanted to suggest as well (centering around C instead of D) 😉

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Posted (edited)

According to my understanding (please correct me if I'm wrong), the centre of the tuning means the point from which you go equal distances in each direction around the circle of fifths. It determines where you meet at the other side of the circle and need to choose between (for example) G# and A-flat. In my case I need neither of those notes except perhaps as very rare accidentals; and anyway a few of the notes in the ad hoc column of my spreadsheet are adjusted from the 1/5 comma ones.

 

A separate parameter is the pitch at the starting point, which in my spreadsheet is A=439: that has no effect on the intervals but obviously affects the departures from ET.

 

I am attaching a modified version of my spreadsheet, with the frequencies in the ad hoc column now entered either as equal to those in the 1/5 comma column (most of them) or as the 1/5 comma ones plus or minus an offset. I have also further tweaked a few of the values.


The frequencies in the 1/5 comma column for all notes were already relative to A, going one way round the circle as far as G# and the other way as far as E-flat.

 

With A set to 439 Hz, making D very close to ET and G slightly above, the average of the differences in column E is zero, and the only differences greater than 7 cents are some of the thirds of the chords, which inevitably depart from the ET pitches to improve the intervals.

 

temperaments - ad hoc.xls

Edited by Richard Mellish
As noted above, the frequencies in my spreadsheet are in fact based on quarter-comma, not fifth-comma

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