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Quarter Comma Meantone - What Root Note?


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A friend is porting Flutini, the real time tuning analyser, to iPod. I recounted that I'd found it useful for checking concertina tuning, and that some concertina players have gone for quarter comma meantone rather than equal temperament, so that if he were intending to offer some temperaments, that would be a potentially useful one. He agrees but asks what root note the temperament should be centred on. Do we have a firm view on this?

 

Terry

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I use A or G or D as my Root note for Meantone tunings, dependant on what other instruments I intend to join with. Some would say it should be C because that is the key in the centre of our 12 note system , ie no sharps or flats, thus a Meantone can be spread evenly through sharp and flat keys.

 

For a Concertina that is to be played with the Pipes, which would be in Just Intonation, then A would be a reasonable Root for 1/4 Comma. Thus for ITM I'd choose A.

There again for a specific Concertina and Pipes duet I would not choose 1/4 Comma.

Edited by Geoff Wooff
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I'd say use A, otherwise your root note would have to be defined by their relationship to A (If you start with a C, how do you get there from say, A=440Hz, by meantone, ET etc.? In this case it would be better to define your C in Hz, as I know some French harpsichordists do.)

More important perhaps is where you put your wolf (sorry Wolf!) - do you go for an Eb or a D#? Ideally you could try to have both, but on a 30 button Anglo, you'd have to choose. (I'd go for D#, on a C/G, to give me a good B natural chord)

 

Adrian

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If Morris dance musicians use C and G, and Irish musicians use G and D (with occasional flirtations both ways from there), is there an argument that G would be a better centre of the universe than C? The Peoples' Key of C, but God's Own Key of G?

 

Terry

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Adrian, do you use A for your tuning regardless of the pitch of the instrument (C/G, G/D, Bb/F, etc), and does your choice of wolf vary with the instrument (eg, having Eb on the Bb/F would seem essential, while having D# on the G/D seems much more useful)? Say one only has one 38-key anglo, in C/G, instead of multiple instruments ... in theory you could have the wolf both ways, choosing Eb in one bellows direction and D# in the other ... though you'd have to train yourself well that they are different notes so you never play the wolf by mistake!

 

Will

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If Morris dance musicians use C and G, and Irish musicians use G and D (with occasional flirtations both ways from there), is there an argument that G would be a better centre of the universe than C? The Peoples' Key of C, but God's Own Key of G?

 

Terry

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?

 

Adrian, do you use A for your tuning regardless of the pitch of the instrument (C/G, G/D, Bb/F, etc), and does your choice of wolf vary with the instrument (eg, having Eb on the Bb/F would seem essential, while having D# on the G/D seems much more useful)? Say one only has one 38-key anglo, in C/G, instead of multiple instruments ... in theory you could have the wolf both ways, choosing Eb in one bellows direction and D# in the other ... though you'd have to train yourself well that they are different notes so you never play the wolf by mistake!

 

Will

 

Yes Will, absolutely, the wolf just follows the circle of fifths around, so on a 30 button G/D, I'd plump for an A# rather than a Bb. On a Bb/F, a C# instead of a Db and on an F/C, a G# and not an Ab. However, as you know, on my 38 button anglos, I have both :-)

 

Adrian

 

Edited to add PS.

 

I should say that I look at my anglos as transposing instruments, in that I read as though they were all in C/G. If I was reading in absolute pitches, I'd of course have a different idea about this.

 

and PPS.

Using a different root note does not alter where you put your wolf, which is a different question, but it will have the effect of lowering, or raising your A pitch standard by a few Hz.

Edited by aybee
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I'm thinking of retuning the brass-reeded Aeola in my avatar to 1/5 comma meantone, centred on G - which is where my voice is centred. I'm after a sweeter tuning for song accompaniment.

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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

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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.

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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, if you remember, it was precisely this problem that led to the Society of Arts Pitch debacle, that is so nicely described on your site (under the paragraph "Whoops".)

The PC version of Flutini has the option of setting each note to a given cents deflection from ET, so so long as the Ipod version has this, I don't see any problem. (except for typing in the note values, but perhaps one could save these as personal preferences?) Of course 13 notes to the octave would be a nice feature, but if one could save "MT with Eb" and "MT with D#" etc., it would be easy to switch between them.

 

 

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.

 

Adrian

 

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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.

Edited by Geoff Wooff
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Can't see why not, Chris, as they are just the same notes jumbled around a bit. But let's see what Geoff reports.

 

I made up this chart to help me get my head around the issues of which modes are available. I think it's right - any corrections happily accepted.

 

I've printed it as an image, as I wasn't sure the table would get through the posting process unscathed.

 

post-11004-0-30421800-1397360579_thumb.gif

 

It illustrates the popular four modes (same as Breathnach reported), set against the relevant key and key signature. I've left the two most common Irish keys (G & D) clear in the middle of the table. Self interest at work there.

 

I believe that the table helps remind us that instruments that are largely limited to a few keys (e.g. pipes, whistle, keyless flute) actually have a wealth of modes (flavours) available.

 

And helps answer questions like, if Am is always referred to as the relative minor of C, why do most of my Am tunes have F# in them? Answer is of course, that they are actually A dorian.

 

Terry

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Geoff,

 

I notice the common Irish keys of DGA are firmly inside your "useful" keys list. Would the related minors be also, including the common modes in Irish music..?

Yes Chris,

all the related Minors and Modes will be 'usefull' as well as some (most ?) of the direct Minors I guess ,though I have not checked all of them out yet but, the emotional value of each Mode will be slightly adjusted in its intensity.

This might be a hard nut to chew for almost all of us who have grown up listening to ET music exclusively but when the Modes are played using a pure scale ( Pythagorian or Just Intonation or one of the Mono Chord derivatives) then the relative grades of emotive value are better expressed. So the happy modes will be joyous and the really sad ones can bring on the tears, depending on the sensitivity of the listener. :blink:

 

So a slight change to the warmth of certain intervals in a scale might alter the feeling of a passage of music but I doubt many people would notice... so best not to worry about that. :rolleyes:

Edited by Geoff Wooff
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Thanks Geoff, and great chart Terry!

 

If you were playing in an EQ session how out of tune would you sound if tuned quarter comma meantone and playing in D. Is there a chart on the net some where which lists the deflections from EQ in cents?

Yes there are charts on the web. Go to www.dolmetsch.com/musictheory27.htm there you will find a calculator page that will show you off sets in cents from ET for more Tuning systems than you have all night to plough through.

 

Caveat ITM: If your principle use of Concertina in ITM is playing single line melodies, in 'Session with others, with the very occasional chords then there is little point in going to Quarter Comma .. it is for the beauty of the sweetened chords that one would wish to go a Meantone tempered keyboard.

 

PS; remember that 'all' the keys I'd suggested above are only available for instruments that can have seperate D# and Eb and G# and Ab buttons.

 

PPS. for a solo instrument or one just to sing to... then 1/4 Comma is very nice.... for a compromise , to sweeten things but still be acceptable to play with other instruments then look to 1/5th or 1/6th Comma.

Edited by Geoff Wooff
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