Tchampe, thanks so much for the fascinating insights from your experiences as a musician - for me these snapshots and vignettes of actual practice are pure gold. 

I know the Hermode system is limited - it's a nod in the direction of authentic orchestral intonation while remaining anchored to ET. I don't regard HMT as the way forward though I am blown away, as you were, by Mohrlok's tremendous ingenuity and effort.

Yes I agree there are these two things: what happens when real musicians perform together, and what we computer users can or could or might do to emulate live performances with ever more vivid and valid realism. 

As you point out, strings can elude strict analysis while they're cloaked in lush vibrato, and that's probably one good reason why I enjoyed William's wonderful rendition of Praetorius' dance written in 1611 for, essentially, a wind band. And btw, strings have yet another ace up their sleeve - they can also use so-called "expressive intonation" which involves playing somewhat sharp at judicious moments to enhance the emotional narrative.

My professional background is design engineering (mostly classified) but I've also been an ardent dilettante in music for much of my life. I had my "swords to ploughshares" moment back in 2001 when I realised that my new ruby red iMac, with Logic Audio Platinum 3.5, Reason 1 and a few fragments of crude sample libraries, would let me design and implement my old '70s dream of a composer's virtual instrument. This virtual instrument is used with normal 12-note MIDI keyboards yet can play in a huge number of keys (over 80 at last count) and modulate freely between them on the fly, in any of several different intonation schemas. It's undergoing another major redesign right now, but I'm also having to wait for Apple to fix something they recently broke in Logic's Environment that my design depends on. Eventually I intend to make the design freely available to all - first as a (somewhat huge) Logic Environment template. 

I reckon intonation is, if not the final frontier in the computer music revolution, then certainly a biggie in the near future.

That is an interesting background Macker!  I also played in orchestra, concert band, brass choir, brass quintet, opera orchestra, chamber ensembles, etc. for many years and have to say something similar to tchampe that the tuning is intuitive - so what does that correspond to any system?  It definitely is NOT reproducing a well-tuned piano.  But it may theoretically approach one of the "pure" or "just" intonation systems.  I have never used the hermode system but it is very interesting, and I wish there was something that did tunings in real time for samples, not fixed like the various settings available in VI, but rather constantly shifting based upon the notes being played.  That might be a huge step forward in realism, because it is normal and even instantaneous in orchestral performance.   

William wrote: "I wish there was something that did tunings in real time for samples, not fixed like the various settings available in VI, but rather constantly shifting based upon the notes being played." Check Mohrlok's HMT website, www.hermode.com/index_en.html. What you describe is exactly what he is doing and he demonstrates it primarily with VI renditions of well-known excerpts. How effective his solution is...a matter of opinion, but it is clearly what he is aiming at.  

Duplicate post...can't see how to delete. Sorry

William and tchampe, the extensive experience and skills you both have as musicians remain beyond what music technology can emulate accurately. As you both indicate, the intuitive approach of skilled musicians is sacrosanct and of paramount importance, and that's also probably a strong reason why music theorists and technologists over the centuries have had such difficulty in trying to grasp the whole subject of musical performance as a matter of facts and scientific knowledge.

Tchampe, I guess the skills and beauty of harmony in musical performance have been highly important if not pre-eminent in your experience; and yes, the whole concept of the Hermode system certainly puts the beautification of harmony front and centre. And yet, awkwardly and stubbornly, there remains also that equally important matter of melody, which HMT does little to address, and whose often difficult and highly complicated relationship with harmony has been central in music for millennia.

Somewhat ashamedly, I admit my system can't compete with the superb convenience of HMT in dealing with harmony. But I've approached the technological problem of surpassing ET from a different angle.

In my earliest simple experiments with just intonation I loved the harmony but found myself yearning ever more intensely for a way of moving beyond one key. On a 12-note keyboard tuned to JI there's almost no scope for modulation. I didn't want to go down the path of using weird keyboards that have more levers per octave than the usual 12 - history shows that such exotic keyboards have never been widely adopted. Moreover, I found it extremely difficult to concoct good melodies in JI; unlike PI, JI scales simply don't lend themselves very well to clean, attractive and intriguing melodies. That's when I conceived of a system that could modulate easily AND give the sense of going places, all in real time, like orchestras but unlike ET.

For me I suppose the melodic dimension, especially when modulating through different keys or tonal areas - all properly intoned - has become pretty much essential. That's why I don't find HMT completely satisfying: it doesn't handle my desire for melodic beauty, movement and modulation because it hangs on to ET while it takes care of harmony momentarily in JI. My system can intone harmony ('vertically') in JI while maintaining PI for the ('horizontal') melodic lines and direction in the music, but it can involve a rather busy and sometimes awkward process, unlike the completely automatic HMT.

I'm beginning to consider whether I can add my system to HMT and get the best of both worlds. But in any case, thanks to you two gentlemen, I'm reminded not to neglect the beautification of harmony quite so much as I probably have.

(P.S. For those who don't already know, the Hermode Tuning System has been a built-in feature of Logic since Logic Pro 9. Unfortunately however, I believe it works only with the virtual instruments Apple provide with Logic. It's in Project Settings/Tuning.)

I've been following this thread with keen interest since it lit up. Great discussion!  It intersects with some of my own interests. Macker, if it's not too complex a request to answer, I wonder if you might share some more details as to how you manage the relationship between vertical sonorities in just intonation whilst embroidering melodies in Pythagorean tuning and how that works in practice. If I can get a bit more detail it might be something to code into a plug-in type MIDI processor that could be used outside of the Logic environment and liberated to be active with other virtual instruments such as our VSL ensembles.

And on a light-hearted note... who cares if a performance controller that provides the "levers" allowing a more nuanced approach to tuning is not widely adopted?  I for one have spent most of my creative life designing and building tools to support my practice that would likely not be of that much interest to the creative community at large. But... and this is a profound "but"... they work for me and I can do the things I want/need to do with them.  Unless, of course, the goal is to invent the next big thing in performance interfaces and go into business to promote it. I haven't the time for that kind of career shift anymore! ;-)  I think William might have been one of those who have suggested that I might turn my performance style system for selecting articulations—an articulation engine—into a marketable tool for others to use. I always respond the same... ask someone to pay for the thing you make, and they'll ask you to support their use of it. This is even more of an issue with things made of computational stuff. Just look at our heroic team of developers here at VSL and the constant stream of requests (to put it mildly) to fix what's broken or wonky. It's a full-time job.  I'm content with my home-brew computational luthierie where it just has to work for me, leaving me most of the time for the creative work.

VSL is heading in the right direction with the model presented by the Synchron Player. The next step would be to add some intelligence based on some performance rules for articulation, dynamics, tempo, etc. that can be mapped to custom articulation sets, such as moving through the dimension tree based on the rules.

I've learned much by studying and adapting the work of Anders Friberg and others in developing my performance system.

https://pdfs.semanticscholar.org/a42d/f8c2cbb3fa304b79a5c36b510c412eaa8dbc.pdf

I'd love to be able to incorporate a more sophisticated approach to tuning. Hermode looks doable, although I too find the examples I've heard to be a lot more subtle than I'd hoped. Which brings us full circle to Macker's approach. 

Kenneth that is a great point about having to provide support for anything sold!  The huge amount of work as well as psychological resilience that VSL must have is mind-numbing to me.  The homicidal rage directed at them for slight glitches which result in the loss of three or four minutes time of some user's  "precious" time (as Smeagol might put it) is a case in point.   

Concerning the linear vs. vertical discrepancies in tuning it becomes even more difficult to relate that to the real world examples. I would not be surprised if one could analyze a really good orchestra's performance of a richly harmonic yet highly melodic composition - perhaps Tchaikovsky's 6th as an example - one would find players changing tuning schemes on the fly, using pure or just or even vesitiges of ET depending on what part they are playing.  It is conceivable that ET becomes more prevalent in melodic lines and would be used almost as passing tones that are a little bit out of the tuning schemes of other instruments and yet intuitively accepted as such.  

Kenneth, I’ll try to summarise how I’ve approached the issues of intonation using my Logic Pro-based system (now provisionally called the Situater). This system generates a 14-bit MIDI pitchbend event to accompany each and every MIDI note-on event for all connected instruments, according to what notes (or more strictly, pitch classes) I want played at each moment. Apart from the built in cast-transposer (see below) it’s all manual, in that I don’t try to second guess or mechanise anything done by the user. It can involve quite a bit of extra work and extra thought, and in this respect I suppose it may sometimes be similar to the case of a harp player who has to plan ahead and determine the pedalling to be used in a piece.

 On my global control panel I first select, say, the “Pure Pythagorean” intonation schema, and then select a preset “cast” of 12 notes that are to be “on stage” until replaced by another cast; each note of the on-stage cast is ready to speak immediately if played either from my MIDI keyboard or from a recorded MIDI region in the DAW sequencer. 

 My system currently can play up to 84 pitch classes in PI, 53-edo, Meantone or Helmholtz, all referred to A. (In 53-edo there are only 53 unique pitch classes and whilst the remainder all have unique names they are aliases of some of the unique 53). For instance, in PI, if the preset cast I select is “relative minor harmonic chromatic” and I have the cast-transposition control set to 0, I’ll have the harmonic chromatic scale of A ready on stage for all voices connected to my system. Thus when I play a chromatic scale on my keyboard, the chosen instrument will speak with the following pitch classes, each tuned precisely in PI:-

 A, Bb, B, C, C#, D, D#, E, F, F#, G, G#.

 Now let’s say I want to make an excursion into the key of F minor, for which I need the notes of Gb, Db, Ab and Eb instead of the sharps available in the current cast. So on Situater's paneI I alter the cast-transposition control to -4, thus transposing the cast 4 fifths down to the relative minor harmonic chromatic scale of F (same as putting 4 flats in the key signature, although my system can’t respond to key signatures or accidentals in Logic’s score editor). To select this cast transposition remotely I could touch one pedal on my Studiologic MP-117 organ-style pedal keyboard, or hit a key on another MIDI keyboard or a split section of my main keyboard, or use any other kind of MIDI controller. Having “recast” in this manner, I can now play the notes:-

 A, Bb, B, C, Db, D, Eb, E, F, Gb, G, Ab.

 System-wide recasting occurs very quickly but needs to be done at least a tick or so before the required notes are started. Recasting won’t affect notes currently being sustained; any required retuning only takes effect with the next relevant MIDI note-on in each voice.

 If I want to sketch and experiment with non-standard casts, on Situater's panel I can manually set each of the 12 keyboard notes to play any of 7 named enharmonic varieties associated with each keyboard note. Thus for example, I may choose to make A on the MIDI keyboard play any of the following pitch classes:-

 A\\\, A\\, Bbb, A, Gx, A//, or A///, where each back slash or forward slash denotes a comma down or up, respectively.

 I can save any manually constructed cast as a preset, and select any of 127 preset casts using any MIDI controller. Typically however, I tend to use my go to utility cast of the relative minor harmonic chromatic scale, and simply transpose it as required at opportune moments in a piece.

You asked specifically about how I manage vertical sonorities in JI while intoning horizontally in PI. I’ll try to answer in 2 parts:

 1.  I exploit the little known fact that nested within the PI harmonic chromatic scale, there is a complete JI diatonic major scale and a JI diatonic minor (melodic descending) scale. But they’re not perfect JI. The submediant, mediant and leading note of these nested JI major scales are each about 2 cents off what they should be in pure JI. However, they’re not bad at all and can render very nice clean JI major thirds with very little evidence of beating. Moreover, when using the Cycle of 53 intonation schema, which is an extremely light tempering of Pythagorean fifths and practically impossible to distinguish from pure PI, each of these 3 approximate JI notes is significantly closer to pure JI and the result is, to my ear, wonderfully clean. For example, nested in the PI h-chrom scale of Ab we have:- 

 •  JI C major - C, D, Fb, F, G, Bbb, Cb

 •  JI E minor (melodic descending) - E, Gb, G, Bbb, Cb, C, D

 Thus when I need to change a note to JI I choose (or make) a cast that covers both the PI and relevant JI notes. Sometimes, e.g. in certain Wagner compositions, I use a special preset cast-modifier function that helps to reduce the number of recasts required when encountering the need for lots of different JI notes in pretty quick succession.

 2.  Up to now I’ve simply ignored the fact that horizontally, individual part lines may move across non-PI intervals as a result of adjusting vertical harmony to JI here and there. It seems the ear (mine anyway) isn’t bothered by and often doesn’t even notice that certain lower voice progressions may deviate from pure PI intervals immediately before or after a vertical sonority has been beautified by JI during rendition. I think it’s also largely a matter of composition, in that the top melodic line should be kept free of any need for JI adjustments - unless the composer deliberately chooses otherwise, or perhaps doesn’t understand how musicians actually render the written music in ensemble.

 BUT … tchampe pointed out the interesting case in actual practice where the lead melody line happens to fall on the 3rd of a dominant 7th chord, in which the players handling the root and fifth would squeeze their pitches up a bit so as to leave the lead melody’s third pretty much untouched in terms of its (presumably PI) absolute pitch while the whole chord is nevertheless adjusted sonorously into JI. I must experiment with this technique using my system, try to get the hang of it and find out how it sounds.

 One thing I have discovered from my all too few exercises in programming famous orchestral pieces and comparing them (obsessively rigorously) with recordings of the very best performances I can find (typically Berlin Phil or Vienna Phil): the score as written is not necessarily to be taken as gospel. 

wow, that is way over my head.  

I don't think about music this way - I just do it.  Try to hear it, imagine it and do it.  This stuff sounds very impressive and worthwhile but I can only work by feel...

@William said:

wow, that is way over my head. I don't think about music this way - I just do it. Try to hear it, imagine it and do it. This stuff sounds very impressive and worthwhile but I can only work by feel...

Macker,

Do you have perfect pitch?..just curious.

William and David, it's silly of me trying to describe what my Situater system can do before it's released - of course I'm bound to wear my engineer's hat and thereby unwittingly and unwillingly alienate an awful lot of musicians. It's my fault not yours.

The various realms of theory behind Situater can be a bit gnarly and driving the Situater will involve a steep learning curve for new users. Sorry to say the vast majority of today's youngsters who've got to grips with DAWs and synths and plugins etc, don't stand a chance of understanding the Situater because they don't have much if any relevant music theory under their belts. Nevertheless I'm hopeful that the system will not only find use among some composers and musicians but also inspire - or perhaps provoke - new thinking about intonation among developers of DAWs and virtual instruments. It's clear there's interest in the topic in this forum.

I'll try to desist from blathering any more about the Situater until I've put it out there.

Michael, no I don't have perfect pitch.

Macker, don't desist - it is very interesting and I really appreciate hearing from your scientific viewpoint.  That is a great thing about this Forum.  I hope you do get your system out there but make it like MIR, which is awesomely complex programming but all under the hood so musicians can use it.  I will definitely be a customer.  

Thanks for the detailed response Macker! That's given me some useful perspective on your technique. I particularly found the relationships between JI and PI—where they correspond in useful ways—to be particularly interesting.

Food for the algorithmic grinder at some point, methinks.

Best,

Kenneth.

William, thank you for your kind and encouraging words. I've endeavoured to make the Situater as musician-friendly as possible - I too am  averse to geeky systems when it comes to making music! How well or badly I've done in that aspect will no doubt be clear when the Situater is out in the world.