My experience with 1/5 comma mean tone tuning

[Little John]

It's about a year since I asked for others' experience with using fifth comma mean tone tuning in another thread. The answers I received were sufficiently encouraging for me to take the plunge and have my 48 key Crabb Crane duet tuned to this temperament. I haven't regretted it for a moment.

 

A brief explanation before I detail my experience. The almost ubiquitous equal temperament (ET) tuning has been understood for centuries, but was shunned in favour of other tuning temperaments until the end of the 19th century and beginning of the 20th century. In its favour, ET eliminates the need to distinguish between, for example, F# and Gb and it makes it possible to play equally well in any key on a piano or other keyboard instrument. Against it is the fact that all keys are equally "out of tune" and, in particular, all major third intervals are sharp by about a seventh of a semitone (14 cents).

 

Fifth comma mean tone is but one of many tuning systems ("temperaments") which aim to overcome this problem of the major thirds, but it does so at a price: only six of the twelve keys sound good, but all of them are equally good. However, for most folk musicians (and others) this is no real hardship - how many of us want to play in C# major or Eb minor, for example?

 

So, I go to collect my newly tuned Crane from Alex Holden and play a tune. It doesn't sound any different. I deliberately play the "wolf fifth" interval G# - Eb. Doesn't sound bad really. I play a B major chord where the third has to be Eb rather than the D# it should be. Not that bad.

 

Despite not sounding much different, the Crabb almost instantly becomes my "go to" instrument. Only gradually do I realise that my initial perception was coloured by a lifetime of accepting the nasty intervals foisted on us by ET. It's not so much that the mean tone tuning sounds sweeter as time progresses, but that going back to ET tuning becomes increasing painful. The sweetness of mean tone tuning became instantly acceptable whilst the harshness of ET became only slowly apparent. I think instinctively my ear knew this, but my brain took a few months to overcome sixty-odd years prior experience.

 

What follows is a bit more detailed, so you might want to give up at this point!

 

In my earlier thread I asked two specific questions: (1) what keys will I be able to play in and (2) how will it sound with other instruments?

 

The answer to the first is down to your choice of accidentals. For most people Bb, C#, F# and G# will be obvious choices, but the Eb / D# choice is a bit more difficult. (This isn't a problem for English concertinas or larger Hayden duets which have space for both.) Since I tend to sing in flat keys I opted for Eb. This choice gives me the major keys of Bb, F, C, G, D & A plus their relative minors G, D, A, E, B & F#. This would be perfectly adequate were it not for one quirk: some forms of music like to employ the major seventh in minor keys, usually in the harmony rather than the melody (giving rise in classical music to the distinction between harmonic and melodic minor scales). So some tunes in E minor want a D#. It occurs only rarely in my playing and there are several ways round the problem when it does occur, so I really haven't found this to be an issue.

 

As to the second question, over the past year I've played extensively in a duo with a guitar and likewise in a duo with a melodeon. I've also played in a jazz context with clarinet, trombone and guitar and spent a very pleasant day with a West Gallery band and choir including a vast assortment of instruments. I have never detected any problem with sounding out of tune; nor has anyone I've played with made any comment.

 

One further observation. As the title of Ross Duffin's fascination book on the subject indicates, the problem with ET is that it ruins harmony. Melody is a different issue. In the jazz context I've played in Eb major and C minor, where I have to employ G# for what should be Ab, but as I've been playing only melody it hasn't been in the least bit noticeable.

 

One further oddity, which I can't really explain. In a new tune I was learning an odd chromatic passage called for a Bb minor chord. Unfortunately the third of that chord has to be C# since I have no Db, but it sounds acceptable. The same is true of F minor with a third of G# (not that I've ever used that chord). So the flattened minor third seems to be more acceptable than the sharp major third in, for example, B major. Perhaps someone else can provide an explanation for that.

 

One final point. My experience relates entirely to fifth comma mean tone tuning, which seems to be a common compromise: the major thirds are much sweeter than in ET but not actually "pure". In quarter comma the major thirds are pure whilst the fifths are narrower and the note pitches diverge more from ET. How much these last two factors matter I don't know. Some advocate sixth comma as less extreme than quarter or fifth; but my experience suggests fifth comma is not an any practical sense extreme. In all cases the six major and six minor keys are equally good, but perhaps in sixth comma the other keys are more acceptable. That might be an issue with, say, baroque keyboard music but not one that would trouble most folk musicians.

 

I am tempted to try a duet tuned to quarter comma mean tone, but to be honest I'm content with fifth comma so I'll probably never get round to it. My new Alex Holden 44 button Crane (due to arrive next month) will be tuned fifth comma mean tone.

 

LJ

[SteveS]

Thanks - a very useful insight into your experiences with 1/5 comma MT.
 

For some time I've been thinking to retune the brass-reeded Aeola pictured in my avatar to 1/5 comma MT - this 'tina is the one I prefer to use for song accompaniment having a strong, sweet sound, with a good dynamic range, which I feel suits songs.  I have previously used it for playing Scandinavian folk dance music, so 1/5 comma MT might work well with the harmonies.

I may just bite the bullet and retune this box.

[bax]

I have hated the equal tempered major thirds for decades. I asked Wally Carroll to tune my Anglo in 1/5-comma meantone. (Partly due to discussions here and other places, so thanks!) It matches standard equal temperament at D, so A is ~2 cents flat and G is ~2 cents sharp. The major thirds are noticeably sweeter. I quite like it.

 

I don't notice that it clashes with other instruments, and no one else has commented on it either. I am generally playing Irish traditional, where the key center is near D and pipes and fiddle don't use equal temperament in the first place.

 

The wolf interval is G#/D# and is intentionally not even available on the same direction of the bellows on this one. Now, I do have another instrument with a slightly different 1/5-comma setup where the wolf interval is C#/G# and can be played, and I would call it "awful"!

 

I was tempted to try 1/4-comma meantone to get the just major thirds. But the discrepancy with others is larger. And, the fifths are very commonly used in Irish concertina, and are noticeably flat in 1/4-comma. So I'm not sure it would work out well.

 

Anyway, in my experience so far I would certainly agree that 1/5-comma is a good compromise and not extreme. Would recommend, would let it marry my sister, etc.
 

[PaddyLosty]

Just to add another to the pile, my C/G Crabb that Greg Jowaisas restored for me and tuned to 1/5th comma meantone in the process has been fabulous, and I wouldn't dream of going back to equal temperament if given the choice. The only downside I can think of is when a fiddler wants to tune to my A, I have to give them a D to get things close to A440. 

[Little John]

On 4/22/2019 at 3:19 PM, SteveS said:

I may just bite the bullet and retune this box.

 

Steve - it's one of those things, feels like a really big step to take but afterwards you wonder why you didn't do it sooner. I can't really see a downside to it - only benefits.

 

18 hours ago, bax said:

It matches standard equal temperament at D, so A is ~2 cents flat and G is ~2 cents sharp.

 

I calculated that, for playing in the "English" keys of G and D it is best to centre the tuning on A. That minimises the deviation from ET. Of course, if you habitually play in other keys than these another centre might be preferable. (If it's a C/G concertina and you play mainly in those keys then D is indeed the appropriate centre for tuning.)

 

4 hours ago, Pgidley said:

The only downside I can think of is when a fiddler wants to tune to my A, I have to give them a D to get things close to A440. 

 

See my response above to Bax. My Crane is centred on A so I was able to give a true 440 Hz note to the West Gallery instruments to tune to. That said, if my calculation is correct, his A at 2 cents flat translates to only about 0.5 Hz which I doubt would be noticeable. The "beating" between a true 440 Hz A and the concertina's A would have a two second cycle.

Edited April 23, 2019 by Little John
To clarify.

[bax]

Haha, yeah, I can't tell the difference in the A in an Irish session type of environment. I do try to give people a D if they ask to tune though.

 

The tuning I'm using is most different from ET at C# (4 Hz beat) and especially G# (7 Hz beat). I like the flattish C# but yeah you could get closer to ET for D+G keys by basing at A and compromising the E flat instead.

 

[Richard Mellish]

On 4/22/2019 at 11:50 AM, Little John said:

<snip>This choice gives me the major keys of Bb, F, C, G, D & A plus their relative minors G, D, A, E, B & F#.<snip>

 

In just tuning, one interval is different between a major key and its relative minor. For example in C major C to D is 9/8 but in A minor C to D is 10/9. Just tuning for C major makes the D minor chord (in A minor) wrong. Does 1/5 comma mean tone avoid that problem?

[bax]

3 hours ago, Richard Mellish said:

In just tuning, one interval is different between a major key and its relative minor. For example in C major C to D is 9/8 but in A minor C to D is 10/9. Just tuning for C major makes the D minor chord (in A minor) wrong. Does 1/5 comma mean tone avoid that problem?

 

To a degree, yes. All the fifths are the same except the wolf, so C+G and D+A pairs sound the same, a hair flat of 3/2 - the wonky fifth D+A is the major source of the horribleness of any D triad in just tuning. The major and minor thirds are all equivalent in the central five keys (C,G,D,A,E on my instrument). F and Bb major, B and F# minor keys are edge cases depending how you harmonize. Ab is unusable (wolf fifth) and for the same reason Eb has a wonky IV and C# a wonky V chord so you would want to avoid those keys too I think.

[bax]

To put it a different way, here is how the triads sound:

 

Ab   garbage (major and minor) - can't physically be played on my instrument

Eb   major is good, minor is off

Bb   major is good, minor is off

F    major is good, minor is off

C    major and minor are good

G    major and minor are good

D    major and minor are good

A    major and minor are good

E    major and minor are good

B    minor is good, major is off

F#   minor is good, major is off

C#   minor is good, major is off

G#   see Ab

 

[Little John]

23 hours ago, Richard Mellish said:

In just tuning, one interval is different between a major key and its relative minor. For example in C major C to D is 9/8 but in A minor C to D is 10/9. Just tuning for C major makes the D minor chord (in A minor) wrong. Does 1/5 comma mean tone avoid that problem?

 

I don't know about just temperament, but in mean tone tuning all whole tone intervals are the same as long as you don't step over the break in the circle of fifths. So in my case C# to Eb and G# to Bb would be much wider than the rest. They would probably be tolerable in a melody and they wouldn't crop up in harmony, so it's not that big a problem. Thirds and fifths are where the real problems lie.

 

LJ

[Little John]

18 hours ago, bax said:

To put it a different way, here is how the triads sound:

 

Ab   garbage (major and minor) - can't physically be played on my instrument

...

G#   see Ab

 

 

It depends which accidentals you have on your instrument. If you have and Ab then Ab major should sound good (Ab - C - Eb), but if you haven't (which is probably the case) and have to use G# instead then it will indeed sound awful. G# major will sound awful because the third will be C instead of B#.

 

LJ

[Paul_Hardy]

I'm about to re-tune an English concertina from its current Old Philharmonic pitch (about 35-40  cents sharp of Concert A=440) down to concert pitch. However, the instrument is tuned so that G# and Ab are appreciably different, as are D# and Eb. So I deduce this is currently in some meantone temperament.

 

Having read the rest of this thread, it sounds as if tuning to 1/5 comma meantone with A held to 440, would let me play in all the keys I'm likely to (mainly G, D, A, occasionally Bb, F, C) without being noticeably far away from other ET instruments, but still have purer thirds than ET.

 

My tuning software (TE Tuner or UltraTuner on iPad) don't seem to support 1/5 comma. So I'm looking for a table of cents deviation from ET for the 14 notes of an English Concertina octave. 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!

[alex_holden]

Hi Paul, those figures don't match what I have. I can't think of a short way to explain how I came up with my figures but I think they are approximately correct (it took me about half a day to wrap my head around the maths!). My table is based on a just perfect fifth being 701.955 cents and 1/5th of a syntonic comma being 21.505/5=4.301 cents, so the temperament is built up from a stack of fifths with an interval of 701.955-4.301=697.654 cents.

 

The way I used it in practice was to create two custom temperament tables in Tonal Energy Tuner. One of them has one set of accidentals and the other has the alternate set, and I have to be careful to use the right table while tuning each reed (though in the case of John's instrument I think there was only one reed that used the alternate set, because he has a button with both Eb and D# on it). I used A as the root note as discussed previously.

fifthmeantone.xls

Edited October 31, 2019 by alex_holden

[Geoff Wooff]

Here are the figures  I  use  for  1/5th Comma  Meantone.  One just needs to  use  any  tuner  set to  Equal  Temperament  and  off set   each note  accordingly:

 

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

 

Currently  both   my EC's  are  tuned  in this fashion  and I am  most  content  with the  results, in fact I have exclusively  used   1/5th Comma  for the last  30  years.

[alex_holden]

1 hour ago, Geoff Wooff said:

Here are the figures  I  use  for  1/5th Comma  Meantone.  One just needs to  use  any  tuner  set to  Equal  Temperament  and  off set   each note  accordingly:

 

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

 

Currently  both   my EC's  are  tuned  in this fashion  and I am  most  content  with the  results, in fact I have exclusively  used   1/5th Comma  for the last  30  years.

 

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.

[Geoff Wooff]

1 hour 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 have a second set of figures  suggested  by  Steve  Chambers  where the  Eb's  are  +14  but  I  have  stuck to the   'closer to ET'  format... from  whence I got  it  I  do not recall  but all sounds sweet enough to me.

[SteveS]

4 hours ago, Geoff Wooff said:

Here are the figures  I  use  for  1/5th Comma  Meantone.  One just needs to  use  any  tuner  set to  Equal  Temperament  and  off set   each note  accordingly:

 

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

 

Currently  both   my EC's  are  tuned  in this fashion  and I am  most  content  with the  results, in fact I have exclusively  used   1/5th Comma  for the last  30  years.

Thanks Geoff - very useful.

I'm thinking to tune the Aeola in my avatar to 1/5 comma (this 'tina has non-ferrous reeds).

 

[Geoff Wooff]

21 minutes ago, SteveS said:

Thanks Geoff - very useful.

I'm thinking to tune the Aeola in my avatar to 1/5 comma (this 'tina has non-ferrous reeds).

 

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.

 

Anyone  interested    can listen to  several recordings  of my  Baritone Treble Aeola ( in 1/5th comma  tuning)  on the Tune of the month  forum... starting with  "The Fiery Clockface"  from March 2013  which is embedded  on page  3 , or  some others  on  my  Soundcloud page.

Edited October 31, 2019 by Geoff Wooff