Ezra Sims
I have recently been listening to 'The Microtonal Music of Ezra Sims' alot! I have also been fortunate enough to be in correspondence with the composer, and i've just waded through a packet of articles on his music that he sent me. In my opinion, Sims clearly represents a very strong step forward in the evolution of our Western tone system. He has emerged from the creative crises that was responsible for serialism with a wholly intact understanding of the asymmetrical beauty of a tonality-grounded musical system. He has arrived at his scale of choice in a very natural way - led intuitively by the creative process of composition and listening. He uses intervals from higher up along the overtone series to create an 18 or 24 note scale as a subset of the 72-tone ET octave division he employs. The harmonic structures found in his music are largely generated by the 'combination tones' of seconds(the interval).
This brings up a very important aspect of Sims' music, and the microtonal movement in general. What are combination tones? Combination tones are created (often as much a physchological impression as a sonic phenomenon) by the interaction of two tones. From each generating pair of tones, there are two combination tones: one above(the summation), and one below(the difference). When we say 'summation' and 'difference', we are talking about the harmonic number produced by the harmonic numbers of the two generating tones added to each other or one subtracted from the other. (Example: say we are in the key of C and our generating tones are G and C'. The G comes from the third harmonic of C and the C' comes from the fourth. The summation tone, then, is 3+4=7. The difference tone is 4-3=1. We now have a four note chord as 1/1, 2/3, 4/1, 7/4.) You will notice that we are propelled into the septimal(7-based) region and beyond the range of equal temperament from only the tonic and fifth. When we use more complex generating tones, like seconds, they create more complex(and smaller intervallicaly) resultant chords. This is how microtonal 'space' is created, which allows for further development of melodic and harmonic movement in smaller intervals.
This process of finding the resultant tones is essentially the same as getting a harmonic mean of an interval, a pattern of growth found in the golden ratio/fibonacci sequence phenomenon. To find the harmonic mean of 3/2, for example, we multiply both digits by 2 to get 6 and 4. We then fill in the middle number, 5, and get 4:5:6, or 5/4(major third) and 6/5(minor third). In this way, the next step up the overtone series is generated. From the 3rd harmonic to the 5th. Now, the fifth is taking us to the 7th, we're finding 11 and 13.
Sims is the best example i've heard of all of this, and it's really beautiful music. Do check him out.
This brings up a very important aspect of Sims' music, and the microtonal movement in general. What are combination tones? Combination tones are created (often as much a physchological impression as a sonic phenomenon) by the interaction of two tones. From each generating pair of tones, there are two combination tones: one above(the summation), and one below(the difference). When we say 'summation' and 'difference', we are talking about the harmonic number produced by the harmonic numbers of the two generating tones added to each other or one subtracted from the other. (Example: say we are in the key of C and our generating tones are G and C'. The G comes from the third harmonic of C and the C' comes from the fourth. The summation tone, then, is 3+4=7. The difference tone is 4-3=1. We now have a four note chord as 1/1, 2/3, 4/1, 7/4.) You will notice that we are propelled into the septimal(7-based) region and beyond the range of equal temperament from only the tonic and fifth. When we use more complex generating tones, like seconds, they create more complex(and smaller intervallicaly) resultant chords. This is how microtonal 'space' is created, which allows for further development of melodic and harmonic movement in smaller intervals.
This process of finding the resultant tones is essentially the same as getting a harmonic mean of an interval, a pattern of growth found in the golden ratio/fibonacci sequence phenomenon. To find the harmonic mean of 3/2, for example, we multiply both digits by 2 to get 6 and 4. We then fill in the middle number, 5, and get 4:5:6, or 5/4(major third) and 6/5(minor third). In this way, the next step up the overtone series is generated. From the 3rd harmonic to the 5th. Now, the fifth is taking us to the 7th, we're finding 11 and 13.
Sims is the best example i've heard of all of this, and it's really beautiful music. Do check him out.