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.
