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I’ve been working a lot with a spreadsheet to validate the tuning in cents, as opposed to just listening. Some of the keys just don’t comport well with the 31-limit tonality. While their “interestingness” is high, I think it’s important to hear what they sound like with a more or less historically accurate tuning. I found the last piece, in the key of F major was able to play almost all the just ratios I would have chosen if I didn’t restrict myself to the 16 note scales on the otonal and utonal that are available in 31-limit. But this chorale, “O Welt, ich muß dich lassen”, in the key of A major, just has too many 30-40 cent deviations from what just ratio I would prefer. So I redid the song using Carl Lumma’s VWRT temperament in A. It’s more conventional, and perhaps a lower interestingness, but here it is nonetheless. Three versions, since there is a lot of indeterminacy in the realization.

This is a version includes a modest change in the order of the complexity factors to make it behave less actively in the beginning and grow in complexity towards the end.

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Nun danket alle Gott #5

This is a version that gradually gets more complex throughout the piece, adding new variations as it goes.

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Nun danket alle Gott #4

This is another of Bach’s Chorales, scored for SATB, performed on Prent’s Microtonal Slide Bosendorfer. The title means “Now Thank We All Our God” in English. It uses many of the same techniques as the last few pieces, and similar tuning from the tonality diamond to the 31 limit.

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Nun danket alle Gott #1

Here is a finished version with slides alternating with the eighth note scalar moves (major and minor 2nds only).

This is one of Bach’s Chorales, scored for SATB, performed on Prent’s Microtonal Slide Bosendorfer. The title means “Ah, how fleeting, ah how insignificant” in English. I broke the piece up into its 39 quarter note length segments, and either play it straight, or backwards and forwards using the Markov Chain Drunkard’s Walk.

The tuning is derived from the 31-limit tonality diamond, with each quarter note segment assigned a scale that makes that chord sound best, including with 6/5 and 5/4 thirds, 3/2 fifths, and 7/4 flatted sevenths. That leaves some harsh notes, as the commas between chords are pronounced.

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ach #3

This is one of Bach’s Chorales, scored for SATB, performed on Prent’s Microtonal Slide Bosendorfer. The title means “Ah, how fleeting, ah how insignificant” in English. I broke the piece up into its 39 quarter note length segments, and either play it straight, or backwards and forwards using the Markov Chain Drunkard’s Walk. There are a lot of eighth notes, and in this version they are all discrete notes. I intend to make them have the option of slides in the next version.

The tuning is derived from the 31-limit tonality diamond, with each quarter note segment assigned a scale that makes that chord sound best, including with 6/5 and 5/4 thirds, 3/2 fifths, and 7/4 flatted sevenths. That leaves some harsh notes, as the commas between chords are pronounced. I may go back and make them slide from one chord to another so that they are masked. That’s for another version also.

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ach #1

Here is the piano accompaniment to Gabriel’s Oboe.

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Gabriel’s Oboe Piano Alone #5

This is a transformation of Lo, How a Rose E’re Blooming from the early 1600’s. Tuning is from the tonality diamond to the 31-limit, with each chord chosing the optimal 16 note scale to make the chord sound true. This leads to numerous comma transitions from one chord to another.

I use the Drunkard’s Walk Markov Chain to go forwards and backwards one chord at a time through the piece.

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Lo, How a Rose E’re Blooming #1

This is a transformation of another of my favorite Hymns. The tune is attributed to William Croft (1678-1727). I’m reading about Winston Churchill in William Manchester’s three volume biography, and this hymn is referred to as popular during the Blitz in London 1941-42.

This version uses the Drunkard’s Walk Markov Chain to go forwards and backwards one chord at a time through the piece.

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O God our Help in Ages Past #1

This version is piano accompaniment by itself.

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The Swan Piano Only