1/5 comma meantone - how do I tune it?

[odonovanchris]

I'm looking to tune a concertina in 1/5 comma meantone centered around D and having A as close to 440 as possible. Could someone knowledgeable on the subject explain how to exactly go about this? Was wondering if anyone has a chart of the frequencies in Hz. Or if someone could explain how to create this. I've searched all over and find it generally confusing to understand how to construct it.

 

Do I flatten the 5ths by a syntonic comma in the following order: D-A-E-B-F#-C#-G#-D#-A#-F-C-G ? And then half or double the resultant frequencies into their respective octaves to make up the scales and correct notes on the keyboard?

 

Hoping to wrap my head around this subject. Thank you.

Edited April 22, 2023 by odonovanchris

[Geoff Wooff]

The  simplest  way  is  to  follow  one  of  the  charts  that  have  been posted  on  Cnet  which  show  deviations  ( in Cents)  from  Equal Temperament  for  each  note.    Placing  A  at  440hz    if  you  wish,  then D  will be  2  cents  sharp of  zero ET.  If  you  cannot  find  these   'cent'   charts  then I  can  re post  here.

There are  other  charts,  perhaps  with  frequencies  in Hertz,  on  the  Dolmetsch  website   www.dolmetsch.com .

 

Edited April 22, 2023 by Geoff Wooff

[odonovanchris]

6 hours ago, Geoff Wooff said:

The  simplest  way  is  to  follow  one  of  the  charts  that  have  been posted  on  Cnet  which  show  deviations  ( in Cents)  from  Equal Temperament  for  each  note.    Placing  A  at  440hz    if  you  wish,  then D  will be  2  cents  sharp of  zero ET.  If  you  cannot  find  these   'cent'   charts  then I  can  re post  here.

There are  other  charts,  perhaps  with  frequencies  in Hertz,  on  the  Dolmetsch  website   www.dolmetsch.com .

 

Thanks! I didn't see the charts before. That helps a lot.

[Paul_Hardy]

I've retuned two instruments to 1/5 comma meantone, and wrote up what I did at https://pghardy.net/concertina/lachenal_27590/lachenal_27590.html#fifthcomma

[odonovanchris]

55 minutes ago, Paul_Hardy said:

I've retuned two instruments to 1/5 comma meantone, and wrote up what I did at https://pghardy.net/concertina/lachenal_27590/lachenal_27590.html#fifthcomma

Amazing thanks!

[Paul_Hardy]

I've done some updates to https://pghardy.net/concertina/lachenal_27590/lachenal_27590.html to clarify the sections on 1/5 comma meantone.

Edited April 23, 2023 by Paul_Hardy

[David Barnert]

3 hours ago, Paul_Hardy said:

I've done some updates to https://pghardy.net/concertina/lachenal_27590/lachenal_27590.html to clarify the sections on 1/5 comma meantone.

 

Nice, but one small point.

 

From your page:

 

Quote

... equal temperament (which is 1/11 comma meantone)

 

Shouldn’t that be 1/12 comma meantone? The comma is divided equally between the 12 intervals of the chromatic scale.

[Paul_Hardy]

9 hours ago, David Barnert said:

Shouldn’t that be 1/12 comma meantone? The comma is divided equally between the 12 intervals of the chromatic scale.

 

No, I agree that it seems odd, but see  https://en.wikipedia.org/wiki/Meantone_temperament which says " Equal temperament is roughly the same as 1/11 comma meantone tuning". 

 

The key (I think) is that ET is 12 lots of the Pythagorean comma, but is only 11 lots of the Syntonic comma.

• The Pythagorean comma is the small interval  in Pythagorean tuning between two enharmonically equivalent notes such as C# and Db.
• The syntonic comma is the difference between the Pythagorean tuning and Just tuning of the major third.

 Meantone tuning definitions are derived from Just tuning, using the Syntonic comma.

 

In Pythagorean tuning, two half tones don't equal a whole tone. In Just tuning, there are two sizes of whole tone. As a useful web resource, see https://mathcs.holycross.edu/~groberts/Courses/MA110/Lectures/PythScale-web.pdf. 

 

I agree that this is a very confusing topic, and I barely manage to understand it. If I get time tomorrow, I'll follow up with a bit more explanation. Or are there any tuning experts here who can explain more clearly than me?

[David Barnert]

Thanks.