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1/5 Comma Meantone

meantone ec tenor-treble

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#37 Geoff Wooff

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Posted 07 June 2016 - 05:32 AM

Hmmm. Now I'm even more confused Geoff. Isn't the "reference zero" note you mention the same thing as the "center point, key or note"?


Not necessarily Jody. Let me try to explain:

The centre point (or Key) I use on the EC is C. this equispaces the useable keys like this ; AB,Eb,Bb,F,( C ),G,D,A,E , so we have four Keys sharp and four Keys flat of C.

The 'Reference Zero' note is in regard to the Diapason. So, one might use A as Zero, as in 440hz but A is, in a Key sense, not so close to C. So one could choose a different Zero in reference to Standard Pitch. I have used both G and D for this but look what happens:


Note deviations from Equal Temperament with A as Zero ( for 1/5th Comma Meantone).

C= +6 , C# = -8 , D = +2 , D# = -12 , Eb = +12 , E = -2 , F= +8 , F# = -6 , G= +4 , G#= -10 , Ab= +14, A= 0, Bb= +10, B= -4.

With D as Zero; take 2 cents off each of the above. ( meaning to use D as on a Tuner set to Standard Pitch)

For C as Zero subtract 6 cents from each of the above. Etc. Etc. Of course this will make the whole instrument flatter.

This moving of the reference Zero can be used to place the notes in the best possible position for playing with certain instruments that are not tuned to Equal Temperament.

Changing the Key Centre note is usefull if your range of keys is spread more to one side or the other... so on an Ab/Eb anglo it might be better to use Eb as the centre Key and chose a zero note that did not make the concertina too flat or sharp overall in comparison to the International Pitch standard.

PS;

It might be worth a listen to some more recordings I made for the Tune of the month forum... you can find these on Soundcloud.com by searching 'Geoff Wooff'. They are not wonderfull recordings but the one called STE-007 is interesting for this topic because I played the tune in seven different keys in one take. The other 1/5 Comma recordings are Valencia Harbour and STE-031.

PPS;

My reason for using a Meantone temperament on the EC is because the Major thirds are a very easy and usefull harmony , on this keyboard, which sound so horrible in ET especially on a metal ended model. This way I am not restricted by the need to invert chords or otherwise re-arrange harmonies.

Edited by Geoff Wooff, 07 June 2016 - 06:48 AM.


#38 Hereward

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Posted 07 June 2016 - 06:22 AM

I think I should have paid more attention to mathematics when I was at school (a long time ago now). Still, I am trying to keep up with all this interesting information and it's certainly good for the little grey cells.


Edited by Hereward, 07 June 2016 - 08:29 AM.


#39 SteveS

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Posted 07 June 2016 - 06:46 AM


Note deviations from Equal Temperament with A as Zero ( for 1/5th Comma Mezantone).

C= +6 , C# = -8 , D = +2 , D# = -12 , Eb = +12 , E = -2 , F= +8 , F# = -6 , G= +4 , G#= -10 , Ab= +14, A= 0, Bb= +10, B= -6.

With D as Zero; add +2 to each of the above.

For C as Zero add +6 to each of the above. Etc. Etc.

 

Geoff

 

For D=0, shouldn't it be subtract 2 from above
For C=0, subtract 6 from the above.

 

Also are these pitch variations from ET expressed in cents?

 

 

(Ed. I see I posted this after Geoff had edited his post)


Edited by SteveS, 07 June 2016 - 06:47 AM.


#40 SteveS

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Posted 07 June 2016 - 06:49 AM

I'm thinking about tuning the 'tina in my avatar (brass reeds, lovely for song accompaniment) to 1/5 comma.

 

Since I sing in C, G, F and relative minors, I guess centering on C would be best.


Edited by SteveS, 07 June 2016 - 06:54 AM.


#41 Geoff Wooff

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Posted 07 June 2016 - 06:52 AM


Note deviations from Equal Temperament with A as Zero ( for 1/5th Comma Mezantone).

C= +6 , C# = -8 , D = +2 , D# = -12 , Eb = +12 , E = -2 , F= +8 , F# = -6 , G= +4 , G#= -10 , Ab= +14, A= 0, Bb= +10, B= -6.

With D as Zero; add +2 to each of the above.

For C as Zero add +6 to each of the above. Etc. Etc.

Geoff
 
For D=0, shouldn't it be subtract 2 from above
For C=0, subtract 6 from the above.
 
Also are these pitch variations from ET expressed in cents?
 
 
(Ed. I see I posted this after Geoff had edited his post)


Indeed I also realised my mistake Steve but thanks for correcting me anyway.

#42 Geoff Wooff

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Posted 07 June 2016 - 07:02 AM

I'm thinking about tuning the 'tina in my avatar (brass reeds, lovely for singing to) to 1/5 comma.
 
Since I sing in C, G, F and relative minors, I guess centering on C would be best.



Indeed it will , but if I was singing and could dedicate a concertina for accompaniment I would consider 1/4 Comma. Adrian Brown uses this on some of his Anglos and Danny Spooner sings to a 1/4 Comma EC. I would tune my EC's to 1/4 Comma but I use the 1/5 as a reasonable compromise between sweeter Maj.thirds and trouble free playing with other people who are invariably in ET

#43 SteveS

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Posted 07 June 2016 - 07:16 AM

 

I'm thinking about tuning the 'tina in my avatar (brass reeds, lovely for singing to) to 1/5 comma.
 
Since I sing in C, G, F and relative minors, I guess centering on C would be best.



Indeed it will , but if I was singing and could dedicate a concertina for accompaniment I would consider 1/4 Comma. Adrian Brown uses this on some of his Anglos and Danny Spooner sings to a 1/4 Comma EC. I would tune my EC's to 1/4 Comma but I use the 1/5 as a reasonable compromise between sweeter Maj.thirds and trouble free playing with other people who are invariably in ET

 

Thanks Geoff - 1/4 comma was something I'd also considered.

I need to do more research I guess...



#44 DaveM

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Posted 07 June 2016 - 09:00 AM

Geoff,

What makes a key "usable" on EC, in meantone?

 

(btw, I think you balked at my table of "number of fifths away from reference" thinking that they were cents deviation; I've since amended the post).



#45 Geoff Wooff

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Posted 07 June 2016 - 01:20 PM

Geoff,
What makes a key "usable" on EC, in meantone?
 
(btw, I think you balked at my table of "number of fifths away from reference" thinking that they were cents deviation; I've since amended the post).


Opps yes Dave,
I got the wrong gist of your post there alright... sorry.

The problem with Meantone systems is that by adjusting note pitches to provide sweeter intervals in certain Keys , some other Keys have to suffer. In the case of an EC, with its seperate buttons for Ab and G#, D# and Eb the well tuned Keys can be extended by one in each direction... one flater key and one sharper.

Whilst one can make a good major scale as far flat as the key of Ab and as sharp as the key of B, when one wants to make a simple accompaniment in those keys and need to employ chords of Db and F# for the purpose the results start to become quite sour. This limits the usable Keys in Meantone on the EC to Eb,Bb,F,C,G,D,A and E majors and their relatives.

With out the enharmonic notes, ie by choosing to tune either an Eb or a D#, an Ab or a G# as one might need to do on an Anglo or Duet, the range of usefull keys would be reduced by one in each direction.

Of course if one is utilising chords further away from the Key note of a tune or modulations occur then further limits on usefull Keys will be imposed.

Edited by Geoff Wooff, 07 June 2016 - 01:22 PM.






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