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  • Getting Real Orchestral Intonation into MIDI Mockups.

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    Part 1. Some Concepts

    The Start of My Long Journey

    Back in the '70s I bought an old upright piano. I soon got busy trying to tune it, based only on my vague recollection from school about "the cycle of fifths". In my ignorance I tuned each successive fifth for perfect consonance! After the second extremely careful attempt I realised I was no nearer to getting the cycle to close, and that I needed to learn more - probably much more - about tuning. So to start with I bought Hermann Helmholtz's classic text, "On the Sensations of Tone".

    Thus began my years of studies and adventures in the realm of musical intonation, which still engages and fascinates me today.

    Which Intonation Schema for Orchestras?

    Still in the '70s, I conducted a multitude of experiments involving many accurate retunings of the 12 analogue oscillators of my Vox String Thing synthesiser, such that I could devise and play at least some fragments of "properly" intoned musical modulations. Those experiments, together with many years of listening experience of recorded orchestral music, convinced me that Equal Temperament - whilst supremely convenient - is too much of an artistically inadequate, aesthetically specious and culturally stultifying means of trying to mimic real orchestral intonation. Perhaps an edifying analogy is today's widespread consumption of ultra-processed food and the all too frequently ruinous long-term consequences for consumers' health and vitality.

    I very soon lost interest in trying to use any kind of novel intonation schemas for orchestral music. I regard novelties of that type as (1) mere pipe dreams; or (2) the result of breaking off engagement with the 'normal cultural standards' of tonal experience, either deliberately (e.g. microtonalists) or neglectfully (e.g. failing to keep a mechanical or analogue instrument properly in tune); or (3) toxic ideas of those unfortunates who are somehow bereft of - and/or hostile to - any substantial, natural, deep-rooted cultural underpinning.

    Orchestral music is - like proper yet creative spoken language and healthy eating habits - the result of very long-term cultural development. And culture, as the natural and ultimate model of democracy, over the long term has always successfully resisted being subjugated to individual willpower. In short, orchestral intonation is not up for grabs. The only innovation I want to see succeed in this cultural domain is the demise of the the innovation of using Equal Temperament to mimic orchestral intonation.

    The intonation schema that has had the longest and most substantial presence in European music history and has for many centuries been the lingua franca of our written orchestral music, is the Pythagorean schema. But additionally, in orchestral rendition, the Pythagorean schema is very often modified by elements of Just Intonation. Customarily the application of these complementary Just elements is not notated but left to the musicians to decide where and when to apply them, in order to best serve the interests of keeping the overall sound - aesthetically and acoustically - as clean and clear as possible.

    According to the music historians who publish their research in their "Early Music Sources" channel on YouTube, it appears there is no historical evidence whatsoever of theoretically pure Just Intonation ever having been used in Europe as a principal intonation schema in its own right. And there's good reason for that absence. In both theory and practice, Just intonation is seriously vitiated by its ungainly and inconvenient intrinsic exigencies: e.g. the prospect of so-called "pitch migration" across polyphonic progressions, and the prospect of awkward or ugly tonalities in melodic lines.

    Given that the concept of a Just Intonation schema as such is very probably merely a fiction contrived intellectually, then unfortunately, dr. Helmholtz was, like Euler et al. before him, barking up the wrong tree. As I know from my own experience it's all too easy to become bewitched and bedazzled by the seductive beauty of the mathematical simplicity and purity of Just intervals. Nevertheless we must strive to recognise that in reality, the very human language of orchestral music is not as simple as that.

    "Existence is beyond the power of words", Lao Tzu said 25 centuries ago. I'll add this corollary: orchestral music can and typically does go beyond the power of small integer ratios. The Pythagorean schema furnishes the complexities and nuances we need if we're to be sensually, emotionally and even viscerally engaged by the music's narrative. Elements of Just intonation help to improve, where appropriate, the music's rendition to be as lucid, palatable and digestible as possible.

    As for Meantone Temperament (explicated mathematically by Zarlino in 1558), it was generally only applied (in its various parametric flavours) to organs and other keyboard instruments, up until around the mid 19th century when it was replaced by the surging trend of Equal Temperament. (Incidentally, it's said that Zarlino set about teaching Meantone to singers, but I've yet to find out what became of that endeavour.) But alas, basically the Meantone Temperament schema is too much of an abstruse mathematical world unto itself and hence, like Equal temperament, tends to be unable to play nicely in concert with orchestral instruments unless modulations and key changes are very mild and kept within a reasonably safe 'sand box'.

    Exotic Keyboards?

    Dr. Helmholtz describes several 19th century designs for exotic keyboards that could play the many notes per octave needed for sophisticated orchestral scores. And I've learnt from elsewhere about other exotic keyboard designs, from recent times and as far back as the 16th century. But the fact remains: none of these exotic keyboard designs have ever been taken up in large numbers. The lesson is clear: the vast majority of keyboard players have always been firmly and faithfully espoused to the conventional 12-note keyboard design. I've therefore ruled out using any exotic keyboard solution for my purposes.

    My main quest soon took shape:- how can a normal electronic keyboard with its 12 pitch classes be used in rendering the 29 or so Pythagorean pitch classes that real orchestras can address (assuming good players and good orchestration)?

    In Part 2 I'll cover a few solutions.


  • Part 2 will not be posted in the VSL forum in the foreseeable future.

    Apologies to those who are interested in this topic.