_______ 6. The Devil's Playground - Diablos en Musica PDF Print E-mail
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Saturday, 31 October 2009 10:54

6. The Devil’s Playground - Diablos en Musica

         a. the howling wolf


            Oh, Diamond, Diamond! Thou little knowest what misfortune thou hast      done!

                        Sir Isaac Newton[1]



The very fundamental progression V-I or 3/2 - 1/1 or the tendency of 3/2-15/8-9/8 to move to 1/1 5/4 3/2 and still retain the same proportions is termed a modulation. Similarly I-IV retains the same proportions as V-I


            1/1      5/4      3/2      to         4/3      5/3      2/1 


The logic implies that IV moves to bVII in the same way, bVII, bIII, etc. This would not be a problem using a precise calculation of the ratios, but becomes one when one is restricted to 12 pitches and an equal octave. The Lords and Ladies of the Renaissance were disturbed to find that the lovely just major triad, with its harmonious thirds did not sound as beautiful in all keys.


They found within their keyboards was what is called a wolf tone – a  harmony that beats and howls.


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This led to a variety of strategies aimed at permitting more distant modulations while trying to maintain the same perfect ratios.  Some added extra keys to the traditional keyboard. These models did not become popular, though some 17 and 19 keys per octave instruments were built.[2]


Stuck with the big twelve, people began to tinker with the absolute pitches, raising and lowering various relationships by small amounts, lessening the howling at the expense of the pure relationships.


Ultimately the perfect fifth and fourth were sacrificed to preserve the octave, or ‘soured’ in the language of the time. The fifth was crushed slightly, by a few cents, the fourth sharpened all within what was considered to be an ‘acceptable degree’.


A variety of temperaments [mean tone, well tempered] were invented to smooth the dissonances yet preserve at much as possible just relationships. Some composers today, notably Terry Riley, swear by mean tone temperament as superior to ET by virtue that its intervals are more harmonious than those of ET and each key has its own particular flavour or quality.


Many are surprised to learn that Bach’s 48 Preludes and Fugues are written for, as the title clearly indicates, a ‘well tempered clavier’ and not an ‘equally tempered’ one. Chopin’s Preludes likewise take advantage of the colouristic qualities and effects noticeable between various keys in a mean tone tuning system. These colours are lost in ET and as of today, most people, myself included, have not heard the music of Bach, or indeed most western art music[3] in the way that the composers themselves would have heard it, and presumably intended it to sound.


next 6.b. pitchforks: tunings & temperaments

[1] Anecdote from St. Nicholas magazine, Vol. 5, No. 4, (February 1878) :

Sir Isaac Newton had on his table a pile of papers upon which were written calculations that had taken him twenty years to make. One evening, he left the room for a few minutes, and when he came back he found that his little dog "Diamond" had overturned a candle and set fire to the precious papers, of which nothing was left but a heap of ashes.

[2]  Isacoff, 105.

[3]right up into the very late romantic period, for true ET was not perfected until 1917!  Duffin, 112.

Last Updated on Tuesday, 25 May 2010 22:19