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Machine6 – Naima v9

This is a set of three variations on the theme of Naima by John Coltrane, scored for Prent’s Microtonal Slide Bosendorfer. This one is based on two otonalities of the 31-limit tonality diamond. Variations 1 and 3 use 8:5 otonality, and the second variation uses the 16:15 otonality. The two have many notes in common, and many that differ by a few tens of cents. There are some intervals that might sound “out of tune”, but I have faith that should John Coltrane, McCoy Tyner, Jimmy Garrison, and Elvin Jones find a way to listen, they would approve. I actually studied with Jimmy Garrison at Bennington in the 1970’s. He convinced me in his own unique way, that I was not destined for a career as a flute player, or jazz musician.

Here’s a chart with the deltas.

And the score from a fake book.

or download here:
Machine6 – Naima v9

Machine6 – Naima v4

This is a set of three variations on the theme of Naima by John Coltrane, this time scored for Prent’s Microtonal Slide Bosendorfer. There aren’t any slides this time, but I plan to do another version with slides. This one is based on two otonalities of the 31-limit tonality diamond. Variations 1 and 3 use 8:5 otonality, and the second variation uses the 16:15 otonality. The two have many notes in common, and many that differ by a few tens of cents. Here’s a chart with the deltas.

or download here:
Machine6 – Naima v4

Machine6 – Naima v2

This is a rendition of John Coltrane’s wonderful tune Naima, named after his wife. It’s so sweet. But the harmonies are quite complex. Every version of sheet music that I’ve seen has a different set of chords. I suppose trying to nail down the chords that McCoy Tyner is playing at any given time is a fools errand. I settled on this one, mostly in Bb, on an otonal scale based on 8:5. The key signature of the first stanza is correct, and should be used on the others as well. It’s not correct on the rest of the piece. Cheap fake book mistake.

I play it here with my finger piano samples.

or download here:
Machine6 – Naima v2

Machine4 – Goldberg Aria and Variations 1-8 v30

This version has a very small change for the E minor chords. I was using the 3:2 otonality (which is a available with a 31-limit tonality diamond based on 9:8), and I changed that to use the 5:4 utonality based on a 1:1 diamond. This change only affected measures 9, 11, 14,and 21. By doing this, I avoid having an E minor chord with a 680 cent fifth. In measure 24 I kept the old E minor. It sounds better.

Throughout the piece I try to maintain all the keys with pure fifths at 3:2, which are 702 cents, thirds that are either 5:4 or 6:5, and 7ths in subdominant chords as 7:4, while preserving the same key notes in the major key of the piece. That means I try to have important notes like the D as 204 and G as 702 cents not change as I move across different chords. Mostly.


or download here:
Machine4 – Goldberg Aria and Variations 1-8 v30

Machine4 – Goldberg Aria and Variations 1-8 v29

I recently discovered that the table I’ve been using for the pitches in the tonality diamond to the 31-limit should have started with a zero value. As a result, all the notes are one step away from where they should have been. Since this is not an equal tones to the octave scale, that’s a big problem. This is the way it used to look:

f3 0 256 -2
0.0016727 0.0033617 0.0054964 0.0056767 0.0058692 0.0060751 0.0062961 0.0065337 0.0067900 0.0070672
0.0073681 0.0076956 0.0080537 0.0084467 0.0088801 0.0093603 0.0098955 0.0104955 0.0111731 0.0115458
0.0119443 0.0124712 0.0128298 0.0133248 0.0138573 0.0144353 0.0150637 0.0157493 0.0159920 0.0165004
0.0170424 0.0173268 0.0176210 0.0182404 0.0189050 0.0192558 0.0196198 0.0203910 0.0212253 0.0216687
0.0221309 0.0241174 0.0249171 0.0241961 0.0247741 0.0253805 0.0256950 0.0258874 0.0266871 0.0275378
0.0277591 0.0281358 0.0289210 0.0294135 0.0297513 0.0301847 0.0304508 0.0315641 0.0327622 0.0330761
0.0336130 0.0340552 0.0347408 0.0352477 0.0354547 0.0359472 0.0365825 0.0369747 0.0372408 0.0374333
0.0386314 0.0399090 0.0401303 0.0404442 0.0409244 0.0417508 0.0424364 0.0427373 0.0435084 0.0441278
0.0443081 0.0446363 0.0454214 0.0459994 0.0464428 0.0467936 0.0470781 0.0475114 0.0478259 0.0498045
0.0516761 0.0519551 0.0524319 0.0525745 0.0528687 0.0532428 0.0536951 0.0543015 0.0551318 0.0556737
0.0558796 0.0563382 0.0568717 0.0571726 0.0582512 0.0591648 0.0593718 0.0597000 0.0603000 0.0606282
0.0608352 0.0617488 0.0628274 0.0631283 0.0636618 0.0641204 0.0643263 0.0648682 0.0656985 0.0663049
0.0667672 0.0671313 0.0674255 0.0676681 0.0680449 0.0683249 0.0701955 0.0721741 0.0724886 0.0729219
0.0732064 0.0735572 0.0740006 0.0745786 0.0753637 0.0756919 0.0758722 0.0764916 0.0772627 0.0775636
0.0782492 0.0790756 0.0795558 0.0798697 0.0800910 0.0813686 0.0825667 0.0827592 0.0830253 0.0834175
0.0840528 0.0845453 0.0847524 0.0852592 0.0859448 0.0863870 0.0869249 0.0872478 0.0884359 0.0895492
0.0898153 0.0902487 0.0905865 0.0910790 0.0918642 0.0922409 0.0924622 0.0933129 0.0941126 0.0943050
0.0946195 0.0952259 0.0958039 0.0960829 0.0968826 0.0978691 0.0983313 0.0987747 0.0996090 0.1003802
0.1007442 0.1010950 0.1017596 0.1024790 0.1026732 0.1029577 0.1034996 0.1040080 0.1042507 0.1049363
0.1055647 0.1061427 0.1066762 0.1071702 0.1076288 0.1080557 0.1084542 0.1088269 0.1095045 0.1101045
0.1106397 0.1111199 0.1115533 0.1119463 0.1124044 0.1126319 0.1129328 0.1132100 0.1134663 0.1137039
0.1139249 0.1141308 0.1143243 0.1145036 0.1166383 0.1183273 0.1200000

And this is the way it should have looked:

f3 0 256 -2
0.000 0.0016727 0.0033617 0.0054964 0.0056767 0.0058692 0.0060751 0.0062961 0.0065337 0.0067900 0.0070672
0.0073681 0.0076956 0.0080537 0.0084467 0.0088801 0.0093603 0.0098955 0.0104955 0.0111731 0.0115458
0.0119443 0.0124712 0.0128298 0.0133248 0.0138573 0.0144353 0.0150637 0.0157493 0.0159920 0.0165004
0.0170424 0.0173268 0.0176210 0.0182404 0.0189050 0.0192558 0.0196198 0.0203910 0.0212253 0.0216687
0.0221309 0.0241174 0.0249171 0.0241961 0.0247741 0.0253805 0.0256950 0.0258874 0.0266871 0.0275378
0.0277591 0.0281358 0.0289210 0.0294135 0.0297513 0.0301847 0.0304508 0.0315641 0.0327622 0.0330761
0.0336130 0.0340552 0.0347408 0.0352477 0.0354547 0.0359472 0.0365825 0.0369747 0.0372408 0.0374333
0.0386314 0.0399090 0.0401303 0.0404442 0.0409244 0.0417508 0.0424364 0.0427373 0.0435084 0.0441278
0.0443081 0.0446363 0.0454214 0.0459994 0.0464428 0.0467936 0.0470781 0.0475114 0.0478259 0.0498045
0.0516761 0.0519551 0.0524319 0.0525745 0.0528687 0.0532428 0.0536951 0.0543015 0.0551318 0.0556737
0.0558796 0.0563382 0.0568717 0.0571726 0.0582512 0.0591648 0.0593718 0.0597000 0.0603000 0.0606282
0.0608352 0.0617488 0.0628274 0.0631283 0.0636618 0.0641204 0.0643263 0.0648682 0.0656985 0.0663049
0.0667672 0.0671313 0.0674255 0.0676681 0.0680449 0.0683249 0.0701955 0.0721741 0.0724886 0.0729219
0.0732064 0.0735572 0.0740006 0.0745786 0.0753637 0.0756919 0.0758722 0.0764916 0.0772627 0.0775636
0.0782492 0.0790756 0.0795558 0.0798697 0.0800910 0.0813686 0.0825667 0.0827592 0.0830253 0.0834175
0.0840528 0.0845453 0.0847524 0.0852592 0.0859448 0.0863870 0.0869249 0.0872478 0.0884359 0.0895492
0.0898153 0.0902487 0.0905865 0.0910790 0.0918642 0.0922409 0.0924622 0.0933129 0.0941126 0.0943050
0.0946195 0.0952259 0.0958039 0.0960829 0.0968826 0.0978691 0.0983313 0.0987747 0.0996090 0.1003802
0.1007442 0.1010950 0.1017596 0.1024790 0.1026732 0.1029577 0.1034996 0.1040080 0.1042507 0.1049363
0.1055647 0.1061427 0.1066762 0.1071702 0.1076288 0.1080557 0.1084542 0.1088269 0.1095045 0.1101045
0.1106397 0.1111199 0.1115533 0.1119463 0.1124044 0.1126319 0.1129328 0.1132100 0.1134663 0.1137039
0.1139249 0.1141308 0.1143243 0.1145036 0.1166383 0.1183273 0.1200000

I noticed that there was something wrong with the G major based on the 1:1 otonality. The B a 5:4 above the G sounded wrong. The G was using 127th value in the table, for a value of 0.0701955, but the 127th value in the old table was 0.0721741. The same offset made the B, which was the 198 value in the table should have been using the value of 0.1088269, but in the old table, the 198th value was 0.1095045.

So basically whenever I thought I was playing a G 3:2 above 1:1 C, I was playing a 44:29, and the B should have been 15:8 above 1:1, I pulled a 32:17. That made a major third of 373 cents instead of the 386 that is the just 5:4. That’s a difference of 13 cents. Some intervals are not so bad, but that means all the pieces I’ve made since May of 2017 are full of lots of wrong notes.

I regret the error. I’m going back and redoing some of the pieces to fix the mistake. This might take a while.


or download here:
Machine4 – Goldberg Aria and Variations 1-8 v29

Machine5 – Cleansing Fountain & 16 Variations – v4

Here is another trip through the algorithms of the latest machine. The piece is based on Cleansing Fountain, a traditional song that was included as a quote in the Charles Ive’s song “General Booth Enters into Heaven”. I made the variations by collecting all the notes of each measure into a list, then choosing from that list as I move through the measures. I take four measures at a time for each variation. At the start of the variation, I choose a rhythm, density, randomization algorithm, and volume. Then for each measure, I choose the proper key, measure, and type of measure it is. The type is either C major and G major, F major and C major, or all F major. Those three include all the measures in the piece. Then for each note, I choose an envelope, slide, note, duration, and other factors. I do this for sixteen variations, then restate the last few measures of the song straight. Sometimes the density is sparse, sometimes dense. Sometimes it’s loud, sometimes soft. It all depends on the choices the preprocessor makes. This one is the most recent trip through the machine, fresh today.

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Machine5 – Cleansing Fountain variations v4

Machine5 – Cleansing Fountain & 16 Variations – v3

Here I let the machine make 16 variations on sections of the song Cleansing Fountain. They are anywhere from a few seconds to a little over a minute in length, separated by short silences. Each takes the notes of four of the sixteen measures and scrambles them up in different ways, including sliding from one note to another. I’m still working on this, and think I will have something of interest soon. The tuning is derived from two scales in the tonality diamond to the 31-limit. The scales are either the otonality on 1:1 or 4:3. They share many of the same notes, and I didn’t have to change the value of any note moving from one to the other scale. Some of the variations are very quiet. I think I might need to keep that from happening.


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Machine5 – Cleansing Fountain variations v3