Quarter Comma Meantone - What Root Note?

[cboody]

As has been said ,moving the Root note will only shift the overal pitch of your keyboard up or down and the reason for this is that Meantone systems are constant throughout the limit of their range. They are not temperaments with better or worse intervals depending on the key , untill ,that is, you have surpassed the limit of usefull Keys. That is the idea of their use in keyboard instruments. The Meantones are Regular Temperaments!!!!

 

On a Twelve Tone keyboard (Piano, Harpsichord etc) the tuning compromises of anything other than ET will arrive quickly and it will be necessary to either choose your key or choose how you tune your notes for any given piece of music.

 

On some concertinas ( Englishes and the larger Anglo and Hayden Duets) it is possible to use 14 tones per octave. This will extend the usable Keys of Meantone systems because by having an Eb and a D# , an Ab and a G# it is possible to hide the Wolf Fifth for two more Keys.

 

Although three of my Electronic 'tuners' have programmable temperaments I have , for the most part, choosen to ignore them and use my eyes and brain to set these other temperaments referenced as deviations from ET. I have set up one Tuner to provide two 'Mono Chord' temperaments for quick tuning of my Hurdy Gurdies.... (Mono Chords are types of Just Intonation which sound wonderfull on Drone based instruments which play in a limited range of Keys).The Programable Tuners I have found so far only allow for 12 notes per octave !

 

I have used slightly different Root notes for my Concertinas,only so as to marry certain notes closer to those of instruments that do not use ET... such as bagpipes and hurdy gurdies.

 

PS: I note from trials this morning that Ab is not a viable key in Meantone on my concertinas ( as I had stated on another thread) unless one alternates Ab's with G#'s during a piece which sounds really weird... I did try playing in G# as opposed to Ab but with one I get a good 'third' but a bad 'forth' and vice versa of course. So the limit of 'good' Keys (on the EC in Meantone) are Eb,Bb,F,C,G,D,A,E and B.. I think.

Here's my previous response to Geoff on another thread. It belongs here. That said, I think Geoff is spot on here. Maybe my comments will be useful to someone if only for the references.

 

Hi Goeff,

No, 1/4 comma makes the purity of chords vary more from the home key to keys further away on the circle of fifths. I well remember an old recording discussing temperament. A reed organ was tuned perfectly to 1/4 comma mean G major. "God Save the Queen" was played in G, D, A, E, B, F# and C#/Db. The last of these was termed "a useful but horrible example," and that was certainly true.

Here's an example comparing ET and 1/4 comma. Those "far out" chords will be less objectionable in 1/5 comma.

Edited to add: and this set of examples

http://kevinboone.ne...ament_test.html

And some good discussion here

http://www2.siba.fi/...php?id=50&la=en

Finally, you suggest 11 keys as useful with 1/5 comma while the literature lists 9 with 1/4 comma. All this said though I certainly do agree with you though that the need to match with ET instruments is probably the big determining factor choosing between 1/4 and 1/5 comma.

Now the real question: Did ET phone home in ET??

[Wolf Molkentin]

Thank you Geoff, it seems that overthere is the answer to a million of questions..., starting with the derivation resp. meaning of the term "meantone".

 

Best - Wolf

 

(not possible to provide a hyperlink this morning as it is erased with the preview - ??)

[adrian brown]

ClearTune allows you to set the root yourself, so I'd expect a port of Flutini to be similarly configurable.

 

Jack

 

I had been wondering for a while how the Cleartone app sets it's 'root note', since when I tried it out a while ago, it wasn't behaving in quite the way I'd expected. I thought perhaps the 'temperament key' (as it's called on the App) was just a way of pushing the wolf around the circle of fifths. So I did some investigations as to what happens to the frequencies as you change this setting.

 

I was surprised to see that with this 'temperament' key set to C, which is the default, it's actually A that is then at 440Hz and the wolf is between D#, and Bb.

With the 'temperament key' set to G, it's the E that is tuned to ET at 659.3Hz and A thus rises to 440.9 to Hz, the wolf is then shifted between G# and Eb.

Set to D, gives you B on ET at 493.9Hz, A is then 441.7Hz and the wolf is between Eb and A#

Set to A, it's F# on ET at 740Hz, A is 442.6Hz, the wolf is between Bb and F !!!

 

Going the other way, it again moves the wolf around a fifth at a time, as well as the note fixed to ET.

So set to F, we have D on ET at 587.3Hz, A is 439.1Hz and the wolf between C# and Ab

Bb, G is on ET at 784Hz, A is 438,3Hz and the wolf between F# and Db.

and so on...

 

So although this App maintains a logical progression through the fifth cycle, the only way to change the position of the wolf is by accepting a different A each time, which is of course completely unnecessary. (You can put it anywhere in the circle you want, by simply having a different series of 11 fifths -1/4 commas and 1 fifth +1 3/4 comma.) So far, I've only tried it for their 1/4 comma meantone setting but now I wonder how the temperament presets work on other electronic tuners?

 

So my feeling is that it wouldn't be a great idea to tune an instrument in meantone using the temperament presets on this app, rather work out the cents deflection from ET that you want, and either program the user settings for this, or just read it directly off the dial with the tuner set to ET.

 

 

 

 

Aybee: Yes, but how do you get to your G from say (for arguments sake a-440Hz) Are you going to take an ET whole-tone, meantone (which comma?),or go through 2 perfect fifths (Pythagorean)? If you want to start with G as your root note, perhaps it would then be better to give up defining A in Hz like the rest of the world and define your G in Hz instead?

 

 

Wouldn't it make sense to make sure, whatever root you centre the meantone tuning on, you conspire to make A = 440 (or whatever other pitch you've set it to), on the grounds of "Give me an A"? I admit I haven't thought through the implications of this! Perhaps those who have set instruments to meantone could tell us their approach and the logic they used to get there.

 

 

ClearTune allows you to set the root yourself, so I'd expect a port of Flutini to be similarly configurable.

 

I've asked Dan about this, so we'll see if it's feasible. I imagine porting a PC application to an iPod, he's hoping to cut down on complexity, rather than adding it!

 

Terry

 

 

Terry, I hope this helps your original question? Again my feeling is that any future Tartini App (which I would welcome with open arms), should simply have user definable presets for each note, to avoid this sort of confusion.

 

Adrian

[Terry McGee]

Thanks, Adrian. I've had Dan peering over our collective shoulders during this discussion, and we've had several conversations on it. He has reached a conclusion which hopefully will meet all needs:

 

I had nearly decided to put in an adjustable root for temperaments, given your email. However, the app already has the ability to add new temperaments, which will give someone who really needs a certain setup full control anyway - and they only need to set the thing up once. I think I’ll just keep it that little bit simpler, to avoid the possibility of confusion for users. I’ll try to include whatever versions of, e.g. 1/4 comma meantone, that I gather are in common use.

 

So, if the regime you want isn't included in the app, you can add it and save it. And we know where he lives, so we can easily get on his back if it isn't up to our requirements! I'll let people know when it's available.

 

This of course throws the responsibility for identifying ideal concertina temperaments back onto our community, and we need not be limited to the renaissance-baroque precedents. But we will need to be able to express ourselves in terms of a list of deviations from ET. I don't know to what extent Dan's app will resemble the current Flutini, but here's the current Flutini temperament set up arrangement:

 

 

Terry

[Dave Weinstein]

I have a mid-1850s Wheatstone English that was never tuned out of high pitch meantone.

 

It was one of Greg Jowaisas' Christmas stack a few years back, and if I recall correctly, during restoration it was determined to be in quarter-comma meantone rooted in A (which in fact, it still is).

 

It is mostly limited by my inability to wrap my head around the English layout, it sounds lovely.

 

--Dave

[Smythe Dakota]

Have any of you who have tried quarter-comma meantone ever noticed the extreme beauty of the B-flat seventh chord, and its various inversions?

 

I am assuming the wolf fifth is placed between G-sharp and E-flat. Then the chord Bb-D-F-G# (yes, G#, not Ab) sounds like nothing you've ever heard before! I think it works because a meantone G# is very close to the true seventh harmonic of Bb. This chord reminds me of a fine freight train horn -- especially if you invert the chord so that the G# and Bb are together, for example G#-Bb-D-F.

 

In quarter-comma meantone you can almost play in the key of Eb. Only the Ab note is missing, replaced by G#. A simple melody in Eb major sounds great, as long as the G# note is used only as the seventh in a Bb seventh chord.

 

For that matter, just the two notes G# and Bb sound really good together. It's a wide whole tone, consisting of two diatonic semitones, rather than one diatonic and one chromatic.

 

Try it, you'll like it!

 

Bill Smythe

[alex_holden]

 

Setting the G to the G of ET will keep the deviations of the other notes from ET least problematical when you play with ET tuned instruments. Adjusting things so that A=440 but the G is mean toned from that a will move the pitch center of the instrument a bit away from ET notes based on A=440 (except for the A of course). Whether this will really bother anyone I do not know. I'm not sure how much difference there would be nor whether it would be bothersome. There are pages with the calculations available, and I'd suggest folks check them out. Bothersome though, is in the ear of the listener and I suspect will vary with listeners.

 

Finally, 1/4 comma is lovely, but quite limiting as to key center. If you center on G all chords will sound best. As you move around the circle of 5ths the major chords will become more and more an issue. In D the chords of G and D will be fine with the chord on A being slightly off. In A the D chord will be fine the A chord slightly off and the E chord a bit further off. Etc. So, the best key to center on would be one in the "middle" of the major keys (or perhaps it is better to say the major key signatures) that you play in. If y ou play in C G and D then G would be the best choice. If you play in G, D and A then D would be the best starting point. The differences are not to bothersome if you don't move too far from the tuned key, but get really noticeable as you move away. That is why several folks here have recommended 1/5 comma mean tone tuning. It is not as perfect as 1/4 comma, but less bothersome as you move to "further out" keys. For EC that is particularly important. Were I an anglo player that wanted 1/4 comma I'd probably decide on two instruments and make the starting point different on each. Or, I'd decide, as is often the case with anglo music (cut not always of course) I'd play close to my home keys as discussed above.

I'm sorry, but I hadn't realised that one might tune to meantone, but still want to play with ET instruments. Of course in this instance it might be better to think of tuning your G, or D to ET and then working back from there. with quarter comma meantone, If you took a G, your A would be 7 cents flat or a-438Hz and of your took a D, only 3 cents flat or a-439Hz. However, I have played with other concertinas tuned in ET on occasion, and although you could say it works, it's really far from ideal.

 

I'm building a 30 button Hayden Duet with this button layout:

 

Based on the earlier discussion, if I want to tune this instrument in 1/4 comma meantone, am I right in thinking it makes sense to use G as the root note, with A=438Hz as the pitch reference?

[adrian brown]

 

 

Setting the G to the G of ET will keep the deviations of the other notes from ET least problematical when you play with ET tuned instruments. Adjusting things so that A=440 but the G is mean toned from that a will move the pitch center of the instrument a bit away from ET notes based on A=440 (except for the A of course). Whether this will really bother anyone I do not know. I'm not sure how much difference there would be nor whether it would be bothersome. There are pages with the calculations available, and I'd suggest folks check them out. Bothersome though, is in the ear of the listener and I suspect will vary with listeners.

 

Finally, 1/4 comma is lovely, but quite limiting as to key center. If you center on G all chords will sound best. As you move around the circle of 5ths the major chords will become more and more an issue. In D the chords of G and D will be fine with the chord on A being slightly off. In A the D chord will be fine the A chord slightly off and the E chord a bit further off. Etc. So, the best key to center on would be one in the "middle" of the major keys (or perhaps it is better to say the major key signatures) that you play in. If y ou play in C G and D then G would be the best choice. If you play in G, D and A then D would be the best starting point. The differences are not to bothersome if you don't move too far from the tuned key, but get really noticeable as you move away. That is why several folks here have recommended 1/5 comma mean tone tuning. It is not as perfect as 1/4 comma, but less bothersome as you move to "further out" keys. For EC that is particularly important. Were I an anglo player that wanted 1/4 comma I'd probably decide on two instruments and make the starting point different on each. Or, I'd decide, as is often the case with anglo music (cut not always of course) I'd play close to my home keys as discussed above.

I'm sorry, but I hadn't realised that one might tune to meantone, but still want to play with ET instruments. Of course in this instance it might be better to think of tuning your G, or D to ET and then working back from there. with quarter comma meantone, If you took a G, your A would be 7 cents flat or a-438Hz and of your took a D, only 3 cents flat or a-439Hz. However, I have played with other concertinas tuned in ET on occasion, and although you could say it works, it's really far from ideal.

 

I'm building a 30 button Hayden Duet with this button layout:

Hayden_Duet_1_Button_Layout.gif

 

Based on the earlier discussion, if I want to tune this instrument in 1/4 comma meantone, am I right in thinking it makes sense to use G as the root note, with A=438Hz as the pitch reference?

 

Alex,

 

I think that would probably make the best sense if you want to play with instruments tuned in ET, and having only 2 accidentals, you're not going to be bothered by where to place the wolf interval.

 

Your question got me thinking about meantone temperaments on duets in general - without the enharmonic possibilities of the English system and the larger anglos, it's probably the system least suited to unequal temperaments? Has anyone ever tried it? One work around would be to tune the 'black notes' as enharmonics - say with the flat pulling and sharp pushing. It might take a bit of getting used to, that you would then only ever play a B major chord pushing and a C minor pulling, but I don't see why it wouldn't work.

 

Adrian

[alex_holden]

I think that would probably make the best sense if you want to play with instruments tuned in ET, and having only 2 accidentals, you're not going to be bothered by where to place the wolf interval.

 

Your question got me thinking about meantone temperaments on duets in general - without the enharmonic possibilities of the English system and the larger anglos, it's probably the system least suited to unequal temperaments? Has anyone ever tried it? One work around would be to tune the 'black notes' as enharmonics - say with the flat pulling and sharp pushing. It might take a bit of getting used to, that you would then only ever play a B major chord pushing and a C minor pulling, but I don't see why it wouldn't work.

Thanks Adrian.

 

I'm still trying to fully get my head around unequal temperaments, but doesn't the Hayden layout (theoretically at least, if the keyboard is big enough) have all the enharmonic pairs?

https://en.wikipedia.org/wiki/File:Wicki-Hayden_Musical_Note_Layout.png

[Don Taylor]

 

Your question got me thinking about meantone temperaments on duets in general - without the enharmonic possibilities of the English system and the larger anglos, it's probably the system least suited to unequal temperaments? Has anyone ever tried it? One work around would be to tune the 'black notes' as enharmonics - say with the flat pulling and sharp pushing. It might take a bit of getting used to, that you would then only ever play a B major chord pushing and a C minor pulling, but I don't see why it wouldn't work.

 

Adrian

Adrian:

 

I think that Alex's 30 button Hayden would fill the same sort of slot that 20 button Anglos fill. Not chromatic and only a limited number of the most common 'folkie' keys - C, D and G plus their modes. But small, light and easy to find your way around.

 

So, should it be tuned in 1/4 comma meantone? Well, this 20 button Anglo tuned in 1/4 comma meantone, playing a folk tune sounds good to me.

 

https://youtu.be/nq70e3T7jVo

 

Added later: Perhaps a good reason for meantone tuning on very small concertina is that thirds now sound harmonious and need not be avoided which otherwise would leave very few options on a small box.

Edited April 26, 2017 by Don Taylor

[adrian brown]

 

I think that would probably make the best sense if you want to play with instruments tuned in ET, and having only 2 accidentals, you're not going to be bothered by where to place the wolf interval.

 

Your question got me thinking about meantone temperaments on duets in general - without the enharmonic possibilities of the English system and the larger anglos, it's probably the system least suited to unequal temperaments? Has anyone ever tried it? One work around would be to tune the 'black notes' as enharmonics - say with the flat pulling and sharp pushing. It might take a bit of getting used to, that you would then only ever play a B major chord pushing and a C minor pulling, but I don't see why it wouldn't work.

Thanks Adrian.

 

I'm still trying to fully get my head around unequal temperaments, but doesn't the Hayden layout (theoretically at least, if the keyboard is big enough) have all the enharmonic pairs?

https://en.wikipedia.org/wiki/File:Wicki-Hayden_Musical_Note_Layout.png

 

So it does - how silly of me! I am still trying to get my head around duet layouts! Do the other systems also have all the enharmonic pairs?

 

 

 

Your question got me thinking about meantone temperaments on duets in general - without the enharmonic possibilities of the English system and the larger anglos, it's probably the system least suited to unequal temperaments? Has anyone ever tried it? One work around would be to tune the 'black notes' as enharmonics - say with the flat pulling and sharp pushing. It might take a bit of getting used to, that you would then only ever play a B major chord pushing and a C minor pulling, but I don't see why it wouldn't work.

 

Adrian

Adrian:

 

I think that Alex's 30 button Hayden would fill the same sort of slot that 20 button Anglos fill. Not chromatic and only a limited number of the most common 'folkie' keys - C, D and G plus their modes. But small, light and easy to find your way around.

 

So, should it be tuned in 1/4 comma meantone? Well, this 20 button Anglo tuned in 1/4 comma meantone, playing a folk tune sounds good to me.

 

 

Added later: Perhaps a good reason for meantone tuning on very small concertina is that thirds now sound harmonious and need not be avoided which otherwise would leave very few options on a small box.

 

 

No absolutely Don - I think it would be perfect on a box like this, I can't imagine why you'd tune it (or any 20 key anglo) otherwise.

 

Adrian

[gcoover]

Not to confuse the issue, but several years ago I checked my old Bastari 20-button and it was Pythagorean tuning.

 

Gary

[Don Taylor]

 

I think that would probably make the best sense if you want to play with instruments tuned in ET, and having only 2 accidentals, you're not going to be bothered by where to place the wolf interval.

 

Your question got me thinking about meantone temperaments on duets in general - without the enharmonic possibilities of the English system and the larger anglos, it's probably the system least suited to unequal temperaments? Has anyone ever tried it? One work around would be to tune the 'black notes' as enharmonics - say with the flat pulling and sharp pushing. It might take a bit of getting used to, that you would then only ever play a B major chord pushing and a C minor pulling, but I don't see why it wouldn't work.

Thanks Adrian.

 

I'm still trying to fully get my head around unequal temperaments, but doesn't the Hayden layout (theoretically at least, if the keyboard is big enough) have all the enharmonic pairs?

https://en.wikipedia.org/wiki/File:Wicki-Hayden_Musical_Note_Layout.png

 

 

The 46 button Hayden does not have the enharmonic pairs, a 65 button would but now we are talking about hen's teeth.

 

As for other duets: The 48 and 55 button Cranes do not have enharmonic pairs, some really big Cranes seem to have at least some of the pairs. Looking at Robert Gaskin's chart for an 81-button MacCann I don't see any enharmonic pairs - just G#'s (no Ab's) and Eb's (no D#'s). I stand to be corrected on these instruments.

 

I think that most folks (not all, but most) only use what Brian Hayden calls the "Easy-Peasy" keys on their Hayden concertinas - the keys that all follow the same regular pattern. Although, in theory, a 46 button Hayden is fully (ET) chromatic, in practice I think of it as mainly a diatonic instrument in its easy-peasy keys but in each of these keys any occasionally needed (ET) chromatic note is there, just not in one of the regular places. I suppose that you could play in any of the non-easy-peasy keys on a 46 button, but lots of sharps or even a few flats would have you stretching all over the keyboard.

 

The 46 button easy-peasy keys are all contiguous in the circle of fifths (F, C, G, D, A, E) so, if you accept that you are going to be limited to those keys then why not go with a meantone tuning that works well for for that set of keys and to hell with the other keys? (This is meant as a genuine question, BTW, not a rhetorical question).

 

This post by Geoff seems to say this is possible, in 1/5 comma meantone anyway. In which case, a 46 button Hayden (and the 42 and 52 button Haydens) should be a good candidate for meantone tuning.

Edited April 27, 2017 by Don Taylor

[alex_holden]

No absolutely Don - I think it would be perfect on a box like this, I can't imagine why you'd tune it (or any 20 key anglo) otherwise.

I suppose it depends on whether you're going to be primarily playing solo or in a group with ET instruments. Though perhaps in the middle of a loud session, any slight clashes wouldn't be noticeable anyway.

[adrian brown]

Not to confuse the issue, but several years ago I checked my old Bastari 20-button and it was Pythagorean tuning.

 

Gary

 

But the thirds Gary, they must have sounded dreadful, or did you just leave them out?

 

 

 

No absolutely Don - I think it would be perfect on a box like this, I can't imagine why you'd tune it (or any 20 key anglo) otherwise.

I suppose it depends on whether you're going to be primarily playing solo or in a group with ET instruments. Though perhaps in the middle of a loud session, any slight clashes wouldn't be noticeable anyway.

 

 

I think the way you're proposing to do it Alex, the risk is minimal. At the end of the day strings and woodwinds would adjust to you and playing with accordions or a piano, the difference is so slight that you'd be onto the next note before you noticed! I think the only instrument you'd possibly clash with is another concertina and even then, it's hardly likely to annoy.

 

Adrian

[adrian brown]

 

 

I think that would probably make the best sense if you want to play with instruments tuned in ET, and having only 2 accidentals, you're not going to be bothered by where to place the wolf interval.

 

Your question got me thinking about meantone temperaments on duets in general - without the enharmonic possibilities of the English system and the larger anglos, it's probably the system least suited to unequal temperaments? Has anyone ever tried it? One work around would be to tune the 'black notes' as enharmonics - say with the flat pulling and sharp pushing. It might take a bit of getting used to, that you would then only ever play a B major chord pushing and a C minor pulling, but I don't see why it wouldn't work.

Thanks Adrian.

 

I'm still trying to fully get my head around unequal temperaments, but doesn't the Hayden layout (theoretically at least, if the keyboard is big enough) have all the enharmonic pairs?

https://en.wikipedia.org/wiki/File:Wicki-Hayden_Musical_Note_Layout.png

 

 

This post by Geoff seems to say this is possible, in 1/5 comma meantone anyway. In which case, a 46 button Hayden (and the 42 and 52 button Haydens) should be a good candidate for meantone tuning.

 

 

So what about my suggestion of tuning the enharmonic notes on a duet to different bellows directions? I don't see why it wouldn't work and you could have all 5 'black' notes tuned that way, greatly increasing the number of keys you could use with a meantone temperament. Learning where they are and how you could play certain chords in one direction only would be no more difficult than how anglo players have to remember bellows direction and at least the buttons would be the same for d#/eb, a#/bb etc...

 

Adrian

 

Adrian

[Don Taylor]

In 2016 Geoffrey published a simple list of offsets for 1/5 comma meantone tuning centred on the key of C.

 

Is there a similar list for 1/4 comma meantone?

 

[Don Taylor]

Adrian:

 

"So what about my suggestion of tuning the enharmonic notes on a duet to different bellows directions?"

 

Short answer: I don't know what I think about that. I guess somebody would have to make one and try it out.

 

Don.