Reasons for Change
I have made a couple of comments on this blog suggesting that the tuning system of 12 tone equal temperment that we use almost exclusively is ill-equipped to express new music. Following are some reasons behind these statements.
The first step is to realize how in- and out-of tune 12-ET is. The idea behind temperament is that by compromising the in-tuneness of some of the intervals, we gain a great amount of flexibility in modulation, or moving tonal centers. By making all of the 12 intervals the same size we get 12 keys of equal relationships and the possibility to move freely from one to the next. The problem with this is that musical intervals are not all the same size and cannot be reduced to a common denominator of the equal tempered semi-tone. The purest picture of harmonic structure comes from the overtone series generated by a single fundamental tone. In this form we see the natural musical intervals in all their shapes and sizes well expressed in the whole-number ratios so largely dealt with by the Pythagoreans. The series begins like this:
Fundamental 1/1(C)
Octave 2/1(C)
Fifth 3/2(G)
Octave 4/1(C)
Maj. Third 5/4(E)
Fifth (3/2)(G)
Nat. Seventh 8/7(Bb)
Octave 8/1(C)
Ninth 9/8(D)
...and so on.
These are pure intervals, meaning maximally in tune.
The descrepency of 12-ET in tuning can be great. The first interval we become aware of is the major third, one of the most important intervals in contemporary and classical music. The 12-ET third is approx. 15 cents sharper than 5/4(100 cents being one ET semi-tone). This is quite apparent to the ear, especially with direct comparison. The next is the Seventh. The interval 8/7 is 30 cents low of the ET flat seventh, untouchable on a piano. Along with this specific interval comes other intervals related to and generated by it such as the septimal minor third(the interval of the fifth to the seventh) and a large whole-tone(seventh to octave). As these finer regions of harmony develop, our over-stressed system of 12 equal intervals is quickly left behind.
The question that naturally arises is of course, 'if it is such a flawed system, what about the great works that came out of it?'. One must realize first that this system without question served a purpose and was, in one way or another, completely neccesary. It played it's part in the development of many cultures and thoughts and feelings around the world when those thoughts needed to be thought and the feelings needed to be felt. At this time, however, it's usefullnes is fading, and new musical images are seeking expression. The 12-ET system is deeply connected to the phase of human development that brought about the current world situation, and is in parallel, deeply unbalanced. It really is impossible to seperate a mindset such as capitalistic greed and waste from the tone system of the culture.
Another thing that must be understood is that orchestras don't really play in equal temperament, as it is actually impossible. The musicians naturally tune the chords they are creating through many small ear-based adjustments. The only time a violinist is going to be playing ET intervals is when he/she is paired with a piano to keep them in(or out of) line. These intervals are not distinct enough to be heard truly, but only as shadowy references to real harmonic structure. It is time we came to a system based on experiential truth and expansion, and move away from ignorance and confinement.
More on this topic to come!
The first step is to realize how in- and out-of tune 12-ET is. The idea behind temperament is that by compromising the in-tuneness of some of the intervals, we gain a great amount of flexibility in modulation, or moving tonal centers. By making all of the 12 intervals the same size we get 12 keys of equal relationships and the possibility to move freely from one to the next. The problem with this is that musical intervals are not all the same size and cannot be reduced to a common denominator of the equal tempered semi-tone. The purest picture of harmonic structure comes from the overtone series generated by a single fundamental tone. In this form we see the natural musical intervals in all their shapes and sizes well expressed in the whole-number ratios so largely dealt with by the Pythagoreans. The series begins like this:
Fundamental 1/1(C)
Octave 2/1(C)
Fifth 3/2(G)
Octave 4/1(C)
Maj. Third 5/4(E)
Fifth (3/2)(G)
Nat. Seventh 8/7(Bb)
Octave 8/1(C)
Ninth 9/8(D)
...and so on.
These are pure intervals, meaning maximally in tune.
The descrepency of 12-ET in tuning can be great. The first interval we become aware of is the major third, one of the most important intervals in contemporary and classical music. The 12-ET third is approx. 15 cents sharper than 5/4(100 cents being one ET semi-tone). This is quite apparent to the ear, especially with direct comparison. The next is the Seventh. The interval 8/7 is 30 cents low of the ET flat seventh, untouchable on a piano. Along with this specific interval comes other intervals related to and generated by it such as the septimal minor third(the interval of the fifth to the seventh) and a large whole-tone(seventh to octave). As these finer regions of harmony develop, our over-stressed system of 12 equal intervals is quickly left behind.
The question that naturally arises is of course, 'if it is such a flawed system, what about the great works that came out of it?'. One must realize first that this system without question served a purpose and was, in one way or another, completely neccesary. It played it's part in the development of many cultures and thoughts and feelings around the world when those thoughts needed to be thought and the feelings needed to be felt. At this time, however, it's usefullnes is fading, and new musical images are seeking expression. The 12-ET system is deeply connected to the phase of human development that brought about the current world situation, and is in parallel, deeply unbalanced. It really is impossible to seperate a mindset such as capitalistic greed and waste from the tone system of the culture.
Another thing that must be understood is that orchestras don't really play in equal temperament, as it is actually impossible. The musicians naturally tune the chords they are creating through many small ear-based adjustments. The only time a violinist is going to be playing ET intervals is when he/she is paired with a piano to keep them in(or out of) line. These intervals are not distinct enough to be heard truly, but only as shadowy references to real harmonic structure. It is time we came to a system based on experiential truth and expansion, and move away from ignorance and confinement.
More on this topic to come!
posted by Chris Mosley at 8:40 AM
4 Comments:
You're on a great path here. The 8/7 is actually a major second (approximately 31 cents sharp at 231.17 cents). The minor sevent is actually the inversion: 7/4. Not every melody lends itself to the 7-limit minor seventh. It works well for jazz, but for a lot of "classically oriented" music a 16/9 or 9/5 actually sounds a little better. The ears are ultimately the best judge. These just intervals open up some great harmonic territory. Keep exploring.
you are right. I did mean 7/8(7/4). I agree that it is not always the best choice for a seventh sound. We have grown very fond of the Major 7th(as in major 3rd from the 5th) sound and the natural(7/4) gives what we hear as a dominant. However, the 7-limit intervals give us the beginning of a way out of triadic based harmony. Finer divisions of the octave allow a much greater array of musical spaces to really be developed in similar proportional ways as the triad within the fifth.
thanks for the comment!
More discussions of tuning systems and making microtonal music can be found on the Yahoo Groups. There are two tuning lists. Go to http://groups.yahoo.com/group/MakeMicroMusic/ or http://groups.yahoo.com/group/tuning and sign up to contribute or read about what others are doing in this area.
i actually just joined that group. they definately have alot going on. i will quite likely adopt the 'sagittal' notation system that was developed myself.
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