tones and context

To whom it may concern,

If you are here it may be by mistake or it may be though the so called “microtonal” music or through some other means.  I would like to make some comments about the content here and what to expect in the future.

Firstly, the term “microtonal music” is misleading at best.  It is to imply that the tones used are smaller than usual.   This is only meaningful if it is in reference to another arbitrary system of tuning.  For even if I choose to use a step of 80¢ instead of 100¢, is my tone of 160¢ bigger than something or smaller than something.  The “micro”-tone does not apply in a sense.

I do however intend to explore a multitude of tuning systems and approaches to tuning in my music here, as well as hopefully open some dialogues about tuning, in its practicality, aesthetic, notation, and possibilities.

Some terminology:

edx: equal divisions of x

ed2: equal divisions of the octave (2) .. this is due to the octave being defined as a doubling of a frequency

15-ed2: 15 equal divisions of the octave

just intonation: a tuning system based on intervals which can be described as ratios of whole numbers.   3/2 as the perfect 5th, 5/4 as the major third etc

temperament: a tuning system which equates certain intervals in just intonation so as to manifest different properties.  ie: in meantone temperament the pythagorean major third 81/64 and the just major third 5/4 are equated, removing the syntonic comma of 81:80

from Scott Dakota of the XAII:

“Starting from the beginning with what “temperament” means:

1) We assume pure whole-number frequency ratios as a default or beginning state for our musical intervals. A classic example is “the 5th” in common western musical terms, which is a pure 2:3 frequency ratio in just intonation terms. One can easily tune pure (beatless) 2:3 by ear, and then tune them in chains as long as one likes.

2) With the pure 2:3 ratio, if you tune a chain of those out to 12 notes, the 12th note is *near* being the same pitch as the starting note, but not quite. So one does not actually get the closed cycle of 5ths that people are used to with common 12-equal-temperament, when using pure 2:3 intervals.

3) But if one makes all of the 2:3 intervals slightly flat of pure (about 2 cents flat, a 50th of a common half step), then the 12th note does indeed come back around in the cycle, and is the same as the starting note.

4) To choose to alter a pure frequency ratio beatless musical interval (just intonation) a bit flat or sharp so as to reach some other pitch target, like closing a cycle of 5ths, this alteration is “tempering” pure ratios in service of some overall goal.

5) To give a complimentary example, if we make each 2:3 5th around 3 cents sharp each, we get a different cycle that closes and meets itself at 17 notes. And that is 17-equal-temperament.” – Scott Dakota


comma: the difference between two just ratios

for more please visit:


Some questions I hope to answer:

  1. Can small edx visualizations and ear-training allow for performers and composers to more easily use complex microtonal tunings?   /-/  We already utilize 2-ed2, 3-ed2, 4-ed2, and 6-ed2 as symmetries in our playing.  Would extending this to 5-ed2 and 7-ed2, or a bit further give us potential to divide the octave and other tones in a way that time signatures based in 5 or 7, or polyrhythms as such are common.
  2. Can the study of small equal divisions and regular temperaments lead to a more precise description of functional harmony?  
  3. Does functional harmony exist in the sound continuum?  Is functional harmony related to just intonation or to temperament (or both, or an interaction of both)?  Is functional harmony related to the prime-composition of a rational interval (or an approximation to this)? 
  4. How do approximations/temperings/sense play a role?

Essentially, we would like to: create a notational system which can incorporate any possible system of tuning and be flexible to include further developments as they occur.  We would like this system to be intuitive to sight-singing and to pattern recognition.  We would like this system to have some semblance if possible to conventional notation systems.  We would like this system to be precise and flexible with minimal accidental, but maximal functional properties.

I believe this can be solved through a modulatory perspective.  To state a piece is initially in 15-ed2 with a tonic at A440hz could for example imply a specific notation to a diatonic scale… or to a Porcupine ( or Blackwood ( scale, or possible a 5-ed2 scale, for these are the most fundamental bases of 15-ed2.  With these we could also specify a degree of accuracy in which tuning would be related to just intonation, for example, in a 15-ed2 piece in Porcupine, should perfect fourths be tuned closer to the just 4/3 when possible, or should they maintain strict 480¢.  It is my believe that the understanding of these relations is ultimately much more simple and fulfilling for both performer and composer than a system of an incredible amount of accidentals or perpetual pitch adjustments notated above known pitches.  Those systems are only momentarily utilitarian, but eliminate the performers possibility to play based on contextual relations and knowledge and are forced to be arbitrarily and often inaccurately precise.

Comments and discussion more than welcome



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