Ivor Darreg

Who's Afraid of the Big bad Wolf?

Some new electronic keyboard instrument have recently come on the market, with a feature that commercial instruments previously have not promoted--the ability to recall from their computer-like memories, other tunings than the standard 12-tone equal temperament. However, there is a catch! Let us address ourselves to the Meantone Temperament, which is one of the factory-supplied retunings on at least two of the new instruments. The trouble is that they do not give you all of it--they only give you 12 of its pitches.

The 12-tone equal temperament makes no distinction between such pairs of names as G-sharp and A-flat; but the meantone temperament does. But this factory-supplied version of meantone does not give you both G-sharp and A-flat, or A-sharp and B-flat, or B-sharp and C--it implies that it is impossible to furnish both. True, on most keyboard instruments it is not possible to have both at once because of the way the instrument was built--especially so in the case of pianos with their rigidly-frozen design. In the case of pipe organs it is mainly a matter of expense--indeed, you have to be a bank or a billionaire to afford a pipe-organ these days, the price has escalated so terribly.

I see occasional items about a special pipe organ that has more notes per octave--well and good--Handel's meantone organ has 16 pitches of meantone--but let's stop kidding ourselves!!--how many musicians would ever be allowed to play a REGULAR standard pip organ, let alone one these super-expensive one-of-a-kind deals? To pose the question is to answer it.

In all my 70 years, my times of access to any pipe organ, except for those occasions where I was called in to assist in tuning, were pitifully few, and I know many people who have been starved for organ knowledge because no one would EVER let them touch one! To compose any new music in meantone you would have to have such a thing in your own home or studio--having to travel hundreds of miles just won't wash! After all those decades of composing, I am outraged at the arrogance of those writers who seem to think that every worth composer would get such access.

It's financially impossible, that's why, and it's high time someone said so! If you owned one of these fabulously expensive things, or had charge of it at some church or institution, you would deny access to all and sundry; you would feel the crushing burden of the expense.

Only very recently has home recording been good enough to get new compositions from composer to listeners (the plural is very important) at a place and time where they can listen. Not just recording, but the ability to make multiple copies of the master tape when and as needed.

I have had a few requests to put a piano into meantone, but as stated above, only 12 notes of it and that is not enough. If you have G-sharp you cannot have A-flat because there is no way to rebuild the piano to get more strings and keys in. And no piano factory will do it for any price either. What does that mean in practice? It means that if G-sharp is there for A minor and major, A-flat is not there for C minor. Nor E-flat major, a very common key. Playing G-sharp instead of A-flat with E-flat is a horrible dissonance called a "wolf"--hence our title up there. Playing B and E-flat when there should be a D-sharp is if anything even worse.

The factory-provided retuning of 12 notes to meantone will provide you with enough wolves to fill a Zoo. By the time you read this, there may be quite a number of these factory-provided or software-firm disks or memories offering only the crippled meantone with 12 notes per octave. Before we scold them too much, it's not entirely their fault--there are too many music-theory and other textbooks which omit any reference to the fact that meantone need not have any wolves--all you need to do is have more than twelve pitches per octave.

They never saw such an instrument. They never were told there could be any need for one. The writers of the books were only interested in 200-year-old music or maybe 100 years old. COmposers a century ago still had not exhausted ordinary tuning. There still was something to discover. When tonality as distorted by the 12-tone temperament was approaching exhaustion, then atonality was tried. If Factorial Twelve is 479,001,600--i.e., if there are that many possible 12-tone rows, then it would look on the surface as though composers would never exhaust twelve-tone serialism. Alas! Those compositions sound too much alike. They are further hampered by all the twelve-tone-tempered harmony and melody patterns stored in all of us by the previous compositions of Classical and Romantic masters and their emulators. Now, if Atonality and Serialism are used with new non-harmonic scales, or scales very different in structure from 12-tone, then atonality will progress. No, this is not more silent pen-and-ink propaganda crusading for you to start this: I have already done something about it! I have built instruments in new scales and composed on them and recorded the compositions--not merely writing them down to go in some dark box, or to end up in the City Dump.

When you hear or see the word Meantone, usually it will be in a context of Tradition and Preservation or Revival of the Distant Past. Before Bach is a popular trademark for it. Or Let's pretend we are back in the 17th or 18th century in Europe somewhere. Quaint, Nostalgic, Escape from the contemporary hustle-bustle. The bluffer, the culture-collector, the dilettante, the poseur, the college student going to the reference library and adding historical footnotes to a term paper--these are the people who usually bring up the term.

Those who try the disk for their electronic keyboard with the cripple meantone of only 12 pitches on it will probably do it with a sigh and maybe think "so that's the Wolf! That's what they had to put up with in those bygone days--how glad I am I don't have to!"--and lay it in the back of a drawer somewhere...a passing novelty, fit only to gather dust.

They are really missing something. During the World War II occupation, the Netherlands physicist Adriaan Fokker investigated his predecessor's (Huygens') writings and came upon the proposal for a 31-tone equal temperament, which is almost identical with the meantone system. Theoretically the meantone temperament has no circle. Theoretically, it represents an infinite number of pitches per octave, arranged in a line with neither beginning or end--as many flats as you can't imagine and as many sharps as you can't imagine either because their number is infinite. Now that's now very practical. But suppose you do a little figuring as Huygens and Fokker did, and search for near-coincidences. At the first-first step either back or forward for certain of the common intervals, there is such a near-coincidence and the circle can be closed there to give (with very little error) the 31-tone equal temperament.

Several keyboards exist for this tuning and I have played on two fo them. It is quite possible to re-fret a guitar to it. A computer can be programmed for it. Xylophones and metallophones exist in 31. The truncated 12-note subset of meantone only hinted at another exciting property of the system--a very good representation of the 7th harmonic and intervals derived from it. Higher harmonics are also represented far better than the 12-tone temperament can. Quite a number of contemporary composers have used 31, and there is a Huygens-Fokker Foundation headquartered in the Netherlands, which has a U.S. branch.

In Xenharmonic Bulletin Number Nine, which I published ten years ago, I wrote a long article on meantone and 31-equal, and included frequency tables for tuning either one, showing how tiny the difference between them was. I carried out the strict 1/4-comma standard meantone to 40 pitches so that it would be evident there is little practical audible advantage to be gained by not adjusting the 31-member circle to close. I refretted guitars to 31 for myself and others and have published fretting0tables. I have composed in the system and thus am numbered among the composers using it.

Generally another aspect of Meantone/31 is not mentioned: it has a very calm distinctive mood. This is suitable for existing music except when that music cannot be played with a calm attitude. The contrast with ordinary restless twelve is very great. Fortunately, that is not the only mood-contrast--there are at least a dozen other scales with distinctive moods, so the composer's vocabulary is now multiplied some sixteenfold.

It is a shame that so much negative discouraging misinformation about meantone tuning has been spread. No longer valid because of the new instruments now available, and because no-one has to perform 31 on conventional instruments, therefore no need to retune them to 31 tones per octave, so that psychological, physical, and financial obstacles no longer exist. 31 can used conventional notation, and there are some added accidentals that can be used if one wishe. ALong with 17 and 19, it fits conventional staff notation perfectly.

The meantone system, or 31-equal, is too good and useful to leave it to the backward hidebound traditionalists and those who want to lock it away from contemporary composers and shut it up in their closet or some MUSTN'T TOUCH glass case. This Cult-Religion attitude toward "Tradition" simply cannot be tolerated anymore.

IMPORTANT: The new situation is now a dichotomy! It is no longer a case of 12 vs. meantone or 12 vs. quartertone, or 12 vs. 19 or 12 vs. Just Intonation. It is not a TWO-sided antithesis! It is now a wide-open new field of over a dozen systems, each with its own valuable MOOD, and please do not let anyone spoil your enjoyment or cramp your style!