My experience with 1/5 comma mean tone tuning

[Little John]

6 hours ago, alex_holden said:

 

That's interesting, your figures have less deviation from ET than mine and Paul's figures have more. E.g. your Eb is +12, mine is +14, Paul's is +17.

 

I think Alex's figures are "right" in an academic sense, but one needs to remember that all tuning systems are a compromise as soon as you want to play in more than one key and/or introduce harmony. Geoff's figures might be closer to sixth comma MT and Paul's close to quarter comma MT than to fifth comma, but all three will be better than ET.

 

LJ

[Little John]

20 hours ago, Paul_Hardy said:

... I've found  one table of 12 values, that doesn't distinguish between the G#/Ab and D#/Eb enharmonic pairs.

Eb	Bb	F	C	G	D	A	E	B	F#	C#	G#
16.8	14	11.2	8.4	5.6	2.8	0	-2.8	-5.6	-8.4	-11.2	-14

 

So, can someone who properly understands temperaments, or has done this before, provide me such a table with the 14 note values needed for an English concertina using its enharmonic pairs? Otherwise, I'm going to have to dust off my Python programming, and deduce it it from first principles!

 

Paul, it's quite simple really. On the basis of your table, on the right hand end D# will be -16.8 and on the left hand end Ab will be 19.6. The table simply increases (or decreases) by 2.8 every step. But note from other comments following your post that this might be closer to quarter comma than fifth comma; not that there's anything wrong with that, in fact the major thirds will be sweeter.

 

LJ

[SteveS]

7 hours ago, Geoff Wooff said:

A friend  has  a  metal  ended  64 Baritone  Aeola  with   'Bronze'  reeds.  As far as I recall  I  tuned it down  from  pre war pitch  in  1978  and  I'm told the tuning is still  fine.  The tone was  very  nice  and I can only imagine  what  an improvement  1/5 comma would make.

My avatar TT Aeola has a super tone - ideal for singing, hence the desire to tune to 1/5 comma.

I used to use it for playing for dancing, but that really was too much for the reeds, so I now use a TT Aeola which has steel reeds.

[Chris Ghent]

Because I now often play with a piper who has a lovely Froment set in C I recently tuned my spare concertina to Bf/F. After a little advice taking I decided to make it 1/4 comma meantone as well. The result is unplayable in a regular session whereas when I had it in 1/5 comma meantone it wasn’t too bad. In all other respects it is absolutely wonderful. Chords sound smooth, especially thirds which I would not normally use. It is not only the chords, normal melodic sequences sound sweeter, as if your ears hear the implied intervals and add them up. I find myself thinking of wine writer’s jargon;  hints of dark chocolate and cherry in the lower notes, mellow honey in the midrange and echoes of the trumpets at the gates in the upper ranges, etc... Since I finished it I have found myself avoiding my ET C/G and reaching for the MT Bf/F.

[Geoff Wooff]

13 hours ago, SteveS said:

My avatar TT Aeola has a super tone - ideal for singing, hence the desire to tune to 1/5 comma.

I used to use it for playing for dancing, but that really was too much for the reeds, so I now use a TT Aeola which has steel reeds.

I think  would  follow  Chris'  comments  and tune    that  Baritone to 1/4 comma  if  you intend it for  song accompaniment Steve.

[Wolf Molkentin]

5 hours ago, Geoff Wooff said:

I think  would  follow  Chris'  comments  and tune    that  Baritone to 1/4 comma  if  you intend it for  song accompaniment Steve.

1/4 comma mean tone is really sweet (just clashing with ET, should that be present too)

 

Best wishes - ?

 

Edited November 1, 2019 by Wolf Molkentin

[Paul_Hardy]

On 10/31/2019 at 11:35 AM, alex_holden said:

That's interesting, your figures have less deviation from ET than mine and Paul's figures have more. E.g. your Eb is +12, mine is +14, Paul's is +17.

 

I got those figures from the PDF file in Little John's post at 

 

 

So, LJ has a increasing step of divergence from ET between fifths of 2.8. Alex has 2.346, GeoffW has 2.

 

I'm still not sure I fully comprehend the theory, but if the syntonic comma is 21.5 cents, then 1/5 comma is 4.3 cents. However, the tempering of the fifths is away from Just tuning, not from ET. ET fifths are already tempered from just by 11th of the syntonic comma (ET is 1/11 Comma meantone tuning), so we need to subtract that (1.96 cents), giving about 2.34 cents, which is what Alex has in his table.

 

So my table for the English concertina with 14 notes per octave, and 1/5 Meantone tuning, holding A=440 is 

 

Degree	Note	ET cents	1/5MT	From ET	Whole Cents
1	A	0	0	0	0
2	Bb	100	111.731	11.731	12
3	B	200	195.308	-4.692	-5
4	C	300	307.039	7.039	7
5	C#	400	390.615	-9.385	-9
6	D	500	502.346	2.346	2
7	D#	600	585.923	-14.077	-14
7	Eb	600	614.077	14.077	14
8	E	700	697.654	-2.346	-2
9	F	800	809.385	9.385	9
10	F#	900	892.961	-7.039	-7
11	G	1000	1004.692	4.692	5
12	G#	1100	1088.269	-11.731	-12
12	Ab	1100	1116.423	16.423	16

 

Does anyone disagree with that working?

Edited November 24, 2019 by Paul_Hardy
Correct rounding of G# to -12 not -11

[alex_holden]

13 minutes ago, Paul_Hardy said:

I got those figures from the PDF file in Little John's post [...]

 

So, LJ has a increasing step of divergence from ET between fifths of 2.8. Alex has 2.346, GeoffW has 2.

 

I think John's figures were based on 1/5th of a Pythagorean comma rather than 1/5th of a syntonic comma. I don't remember exactly what the difference is but Wikipedia says a Pythagorean comma is about 23.46 cents, so (23.46/5)-(21.5/11) = about 2.74.

[Little John]

27 minutes ago, alex_holden said:

 

I think John's figures were based on 1/5th of a Pythagorean comma rather than 1/5th of a syntonic comma. I don't remember exactly what the difference is but Wikipedia says a Pythagorean comma is about 23.46 cents, so (23.46/5)-(21.5/11) = about 2.74.

 

That's right. I was in error in using the Pythagorean comma. I agree with Alex's figures (and hence Paul's too). The Pythagorean comma is what you get if you stack 12 pure fifths (the comma being the amount by which the note you return to is sharp of the starting note). The syntonic comma is what you get if you stack 4 pure fifths (the comma being the amount by which the resulting note is sharp of a pure major third).

 

46 minutes ago, Paul_Hardy said:

ET fifths are already tempered from just by 11th of the syntonic comma (ET is 1/11 Comma meantone tuning) ...

 

Yes, but technically I think ET is defined as the fifths being tempered by 1/12 of a Pythagorean comma.

 

As I understand it, ET has a precise definition because it makes playing all keys identical, and 1/4 comma MT has a precise definition because it give pure (just) major thirds in the six usable keys; but the rest like 1/5 comma MT and 1/6 comma MT are essentially arbitrary. They are just nice fractions. No reason you couldn't opt for 2/9 comma, 2/11 comma, 3/14 comma or anything else you fancy.

 

LJ

[Wolf Molkentin]

John, and 1/3 comma mean tone produces „just“ minor thirds AFAIK