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Tedrow G/d Meantone Tuning


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Bob,

 

Thank you, you have just made all the hours sitting and questioning the heck out of my beloved wife and getting the theory and practical into myself worth it. Dirge if you ever want a Maccan tuned in Meantone let me know and I will build one for you. The fun is deciding which one to use and we can have fun with that. The more I research into the different tuning (have to for my harmonica clients) the more interesting it gets. Also the more I am sure that I am going to keep two sets of reed plates for my old Lange Chemnitzer as the Meantone 1/5 A=435 is just such a mellow and warm tone to it.

 

Thank you again, may God bless your hands and your list of orders.

 

Michael

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Hi all,

 

I think there is a lot of confusion in the discussion above, which is not surprising as you will see.

 

Since there now seems to be wide interest in the subject of unequal-temperament for concertinas, some here may appreciate a little more discussion of these issues (in more depth than I took to provide above). It is a complicated subject and it doesn't help that some major music dictionaries and other references that people might logically consult have made gross errors that have propagated in the literature (and in music education generally) for decades. For example, Grove's dictionary and the Harvard dictionary of music both are misleading on different aspects of equal vs unequal temperament, enharmonics, etc.

 

First, if we are going to be very precise in this discussion I should briefly correct a couple of omissions of detail from my own post above. I don't like to edit posts once there has been a reply because this can take all intelligibility out of the discussion as recorded in the thread. See points under * below for these corrections and additions. These points are all for the sticklers; they are important but in an attempt at brevity I didn't want to bog down in them when making a couple points to Bob yesterday.

 

Now, in response to Dirge, Chris, et al:

 

I. Different keys do sound different even in true equal temperament (if the pitch of "A" is kept constant), because they will be placed in a different part of the instrument's range and will require response from different parts of your auditory apparatus. Neither musical instruments nor ears respond linearly (in timbre and other variables) to changing frequency, and sometimes they are spectacularly nonlinear (for that matter, so may be the acoustics of the room). Even if a piano is truly in perfect ET every different key will differ somewhat in timbre (tone quality) as well as frequency. Not to be forgotten is that piano technique involves very different motions in the different keys. For a piano player to truly be playing "the same piece in different keys" with *exactly* the same timing, attack, etc. for each note can be very, very difficult. That also might possibly account for a different mood heard by a listener.

 

II. But there is a different question when the temperament is unequal: whether the relative intervals among the notes of the scale are the same or different when changing key. Actually, in regular meantone temperaments there are no differences in the internal intervals between the key of C (for example) and any other key, *as long as the correct notes are present on the instrument.* If you are playing music that stays in one major key with no accidentals you will be using 7 different named notes, maybe present in multiple octaves. A 1/4 comma meantone temperament with 12 notes to the octave might include the notes: C, C#, D, Eb, E, F, F#, G, G#, A, Bb, B. With these notes you can play in the major scales of Bb, F, C, G, D, and A. Within each of these keys, the pitch relationships among the notes of the major scale will be identical (again, as long as the music requires no accidentals). The average pitch of each of these keys will be different but the internal pitch relationships are the same. So, (except for the real and important issue identified in my paragraph labeled "I" above), every one of these keys should "sound" the same in such a musical test, though the music will be transposed up or down in frequency. In comparing a meantone-tuned piano to an equal tempered piano there will be differences in how individual notes and how individual intervals sound (in general, major thirds much sweeter in meantone, perfect fifths a little more active in meantone since narrower), and also, as I mentioned yesterday, the average pitch of the keys in meantone will be a little different than the average pitch of the keys in equal (the entire scale of Bb on the meantone piano may be on average a little sharp to the same key played on the ET piano, and the entire scale of A may be flat on average relative to the same scale played in ET -- depending on where the "center pitch" of the meantone piano is set).

 

III. Where there are real differences in "the tonal colors of the different keys" that depend on actual *differences in relative sizes of comparable intervals from one key to the next* is in the well-temperaments, modified meantone temperaments, and related tunings. This is a hard concept to grasp. But consider the fifth interval from "doh" to "sol." This has a certain "size" in ET and it is the same in all keys within ET. It has a certain "size" in 1/4 comma meantone (a little less than in ET) and again it is the same in all keys within 1/4 comma meantone (if the "correctly spelled" enharmonic notes are available). But there are other tunings where the fifths are different in "size" from key to key within the same tuning; for example, C to G might be "just," D to A a little narrower (as in ET), E to B narrower still (as in 1/4 comma), etc. In these latter temperaments (including "well-temperaments," which are neither equal-tempered nor regular meantone temperaments), which seem to have been very important in European music from Bach's day or before through the early 20th century (or later :-), there really are "different colors of the different keys" that are due to very different proportions of the intervals of the scale. A lot that has been written about the different "sounds" of different keys dates from the period in which such temperaments were dominant in European art music.

 

Hope this very short discussion might help those who raised questions find their way into the literature on this subject. There is a lot on the web and I like the big book "Tuning" by Jorgenson which your library might have or be able to order for you to study. Here are just a couple interesting links from one google search I ran:

http://www.kylegann.com/histune.html

http://www.albany.edu/piporg-l/meantone.html

http://scilib.univ.kiev.ua/doc.php?6604172

 

 

Paul

 

*

Fine points that should be added to my previous post to make it more precise:

1. Actually there is no circle of fifths in meantone, and I should have re-worded my sentence to prevent that misinterpretation. When I mentioned "circle of fifths," I was getting at how the meantone-tuned concertina will compare with ET instruments as *the latter* move through *their* circle of fifths. In meantone, when you progress along the *chain or spiral* of fifths from Eb, Bb, F, C, G, D, A, E, B, F#, C#, G#, D# you just keep going -- because the D# you just played is well flat of the Eb with which you began.

2. Actually Jeffries and (John, et al.) Crabb may not literally have offered their customers alternate enharmonic A#/Bb that "often" -- these would be the commonest duplicates on their anglo layout if keyed for G and D, but in fact original G/Ds are probably not that common. More precise would be to have written that Jeffries and John Crabb often offered the alternate "re #/mi b" when the anglo was made in the keys of "doh/sol." But I'm not sure this would have gotten across without the concrete example.

Edited by Paul Groff
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. But pieces in Db major are very mellow, and it is just the same key. If Bach had "written" the Prelude instead in Db major, would it somehow sound different? How could that be possible? Is it more to do with our attitude at seeing how it is written and thus the way we play it, rather than the sounds themselves?

I'm not a piano player, not even a musician to speak of, but I think the choice of a key has lots to do with the range of an instrument, that translates to ease of playing and sound qualities.

An instrument with the range of 3 octaves will have such range only in it's "home" key, you shift 5 tones up and it's range from useful tonic is 5 tones shorter. On top of that it may not sound as well up there, or too slow and gritty down the scale.

It's characteristic to all instruments, but especially so for the concertina, where low reeds are not your best friends, and high reeds often either just very poorly set up, or too squeaky and short of volume. So arranger must take this into consideration, and write music in the key best suited for the most advantageous range of notes. It has nothing to do with sharp keys been sharper or flat been flatter. They are not. They sound exactly the same, given suitable sonority, so to speak. Perhaps the only moment where keys are felt is the transition from one key to another.

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"in general, major thirds much sweeter in meantone, perfect fifths a little more active in meantone since narrower"

 

 

Meantone tuning is much easier on the ear than even temperament, but the fifths can sound out of tune, especially in chords..

On a C/G anglo if the G row is (generally with a few exceptions) pitched 6 cents higher than the C row it should be possible to have both 3rds an 5ths in tune. This would need a careful choice of which note to use in any situation, and possible change of chord shapes. It probably wouldn't be suitable for Irish-style playing, would suit some English-styles very well indeed.

Regards, Gill

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