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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

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.

or download here:
Machine5 – Cleansing Fountain variations v4

Here is another trip through the algorithms of the latest machine. This one has some nice busy sections.

or download here:
Machine5 – Cleansing Fountain variations v5

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.

or download here:
Machine5 – Cleansing Fountain variations v3

This is a variation of the Cleansing Fountain. I haven’t decided on the structure. For now, I’m just noodling around with ideas. This one takes the notes of the first full measure and plays around with the durations for about a minute.

or download here:
Machine5 – Cleansing Fountain variation v4

This is a straight rendition of a traditional American song called “Cleansing Fountain”. It has to be the most gruesome lyrics of any in the Christian canon. Charles Ives, in his piece “General William Booth Enters into Heaven”, includes musical quotes from “Cleansing Fountain” and a few other hymns. He doesn’t use the “Cleasing Fountain” lyrics. In his song, he uses excerpts from a Vachel Lindsay poem, “General William Booth Enters into Heaven”, which includes the question, “Are you washed in the blood of the lamb?” General William Booth was the founder of the Salvation Army. The poem is a description of his entry in the heaven.

All this is just to say that the song “Cleansing Fountain” has a history, if only as a quote in a great Ives song, at measures 101 to the end. He wrote it in 1914.

I plan to make some alterations over time.

or download here:
Machine5 – Cleansing Fountain v1

This is a complete version of Bach’s Goldberg Aria, together with variations of my own invention. The form is much like the Goldberg Variations by Bach, except the variations are much different. It starts and ends with the Aria as written, except for the tuning, and the slides, grace notes, modants, and trills which are executed on Prent’s Microtonal Slide Bosendorfer, so they are real slides. The variations are based on eight measure sections of the Aria: measures 1-8, 9-16, 17-24, & 25-32. The order of the variations are 1-8, 9-16, then 1-8 and 9-16 again, followed by 17-24, 25-32, which are also repeated. That makes a total of eight variations, each around two to three minutes long. They are separated from each other by a beat or two, just a short moment of identifiable silence or gap. Each variation chooses its own rhythm, volume, and density. Within the variation, the duration of each measure is from 1 to 32 times normal length. There is also a wide variety of envelopes, from normal piano to more of a bowed sound. The notes of the variations are taken from the actual Aria measures, in new ordering and new rhythms. In other words, the notes are all Bach, but everything else is generated by the algorithm of the preprocessor. I load the notes for each measure into a list and pick randomly from the list when I need a note. The randomizer attempts to peak each note no more often than any other note in the specific list. For example, in measure one, there are 3 G’s, two B’s, one D, and a mordant on A. In my variation I end up with a similar number of these notes, more or less, in a random order.

Mordants are implemented as Csound function tables like the following:

When applied to an A, that function creates a B A B mordant. Here is a trill that takes a note up and down a 27:25.

There are also some glide with vibrato slides like this one:

The tuning is as shown in the image below. The notes are derived from the tonality diamond to the 31-limit, extended to allow scales that are 9:8 above those in the diamond. Think if it as two diamonds on top of one another: one based on C and another on D. I could go on, I suppose, but this extension allows me to continue with the types of harmonies I’ve been playing around with lately, and still be faithful to the keys the composer intended. I just twist them somewhat. Each measure uses one 16 note scale, in order to approximate a diatonic major scale. Measure one for example, is in G major, and the scale derived from the tonality diamond to the 31-limit based on D is called the G otonality (“G oton”). I based the ornamentation on that suggested by CPE Bach.

I made three versions, and posted the one that was most interesting.

or download here:
Machine4 – Goldberg Aria and Variations 1-8 v19

This is another variation, in this case of measures 17-24 of the Aria.

or download here:
Machine4 Goldberg – Var #3 – v13

This is another variation, in this case of measures 9-16 of the Aria. There are lots of leading tones in the Aria, most of which are a 15/16 away from the key of the chord. When these notes are combined into a cluster, it makes for a very strong major 7th chord: 8:10:12:15/8. Since I can make them slide the 15:8 to the 1:1 (key of the chord), they have a very nice feeling of resolution. And it sounds more and more like Harold Budd. I like Budd.

or download here:
Machine4 Goldberg – Var #2 – v12

Here’s a variation on the theme of the Aria from Bach’s Goldberg Variations. It’s not like his variations. I take the notes in each measure of the Aria and load them into an array, and allow the preprocessor to choose the ones it will play from the list using a randomization scheme. I apply another randomization scheme for the durations, and a third to select whether or not a note will play after it’s been chosen. There are a wide variety of different envelopes that can be applied to notes, and variations in the density, and other factors. The result sounds kind of like an ambient piece that Harold Budd might have improvised, if he had access to Prent’s Microtonal Slide Bosendorfers.

My plan, which as always is subject to success or failure of the idea, is to take a few measures of the Aria at a time and find a variation that brings out the harmonies and with potential extensions of the tuning into higher ratios. Variation one works only with the first eight measures, and I’ll see what the next one will chose from.

or download here:
Machine4 Goldberg – Var #1 – v10