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Satanic comma

If an interval in one temperament rounds to an interval in a second lower temperament, and that second interval rounds back to the first, the two intervals are said to be cross-rounding, and have (intervallic) resonance.

[For example,] 10/17 = 7.058824/12... Therefore, the nearest note to 10/17 in 12 is 7/12. 7/12 = 9.91667/17... Therefore, the nearest note to 7/12 in 17 is 10/17. 10/17 rounds to 7/12. 7/12 rounds back to 10/17. 10/17 and 7/12 are cross-rounding and have intervallic resonance.

12/17 rounds to 8/12. 8/12 rounds to 11/17. 12/17 and 8/12 are not cross-rounding and do not have intervallic resonance.

Since it accurately describes the errors from rounding 12-tone intervals into 7 and back, the term “accidental” is sometimes borrowed from history and extended to describe any note in any temperament which isn’t cross-rounding to another. In this case, 12/17 is an “accidental” of 11/17 in the 12-tone scale in 17.

Hence, the dominant scale in a scale class can be seen as a symptom of rounding. The 7 notes in the 7+5 scale in 12 can be gotten from rounding all 7-tone intervals into 12.

In using an equal temperament to represent a list of unequal values, say, just intervals, the “legal” intervals are those in which the difference in representative value between two notes is equal to the value of their difference. This is not to say it is against statute law to play “illegal” intervals, but in the context of LOGIC GRIDS, legal intervals are those allowed by the nature of the grid.

Given this scale, based in D, say in Pythagorean tuning: D Eb E F F# G G# A Bb B C C# D; from the root D, the minor second is Eb, making D-Eb the size of the legal minor second.

The legal minor seconds here would be: E-F, F#-G, G#-A, A-Bb, B-C, C#-D;

And the illegal minor seconds would be: Eb-E, F-F#, G-G#, Bb-B, C-C#; or seven perfect fifths.

Cross-rounding the Brun algorithm far enough will yield the convergence web. Not cross-rounding far enough will yield more liberal logic grids because of a lower number of chromatic intervals.

Consider the major chord convergence in the Brun algorithm:
12, 19, 31, 34, 53, 87, 118, etc.

19 has 1 chromatic interval, 1/19.
Cross-rounding through 31, 19 has two chromatic intervals.
Cross-rounding through 34, 19 has three chromatic intervals.
Cross-rounding through 53, 19 has three chromatic intervals.
Cross-rounding through 87, 19 has three chromatic intervals.
Cross-rounding through 118, 19 has four chromatic intervals.
Cross-rounding through 559, 19 has four chromatic intervals.
Cross-rounding through 796622, 19 has four chromatic intervals.

At the 31 point, the logic grid of 19 is identical to meantone, because of the intervallic paradoxes. At 34, it expands to 3. From 118, the convergence web has been defined.

A square array listing the notes of a temperament on the side and on the top, showing under what circumstances the notes are allowed to pass to one another. These can be either true or false grids, or layered from atonality through preconvergence and convergence webs all the way to serialism, in which, only one note is legal after the current one.

Correct me or excuse me if atonality is the wrong word, but I’m speaking of the legal system in which any note may follow any note and any note may be harmonized with any note. The logic grid for these conditions would be filled with “true”.

Consider the major chord convergence in the Brun algorithm:
12, 19, 31, 34, 53, 87, 118, etc.

19 has 1 chromatic interval, 1/19.
Cross-rounding through 31, 19 has two chromatic intervals.
Cross-rounding through 34, 19 has three chromatic intervals.
Cross-rounding through 53, 19 has three chromatic intervals.
Cross-rounding through 87, 19 has three chromatic intervals.
Cross-rounding through 118, 19 has four chromatic intervals.
Cross-rounding through 559, 19 has four chromatic intervals.
Cross-rounding through 796622, 19 has four chromatic intervals.

A layered logic grid would show:

An imagined or forced behavior, in a preconvergence web, in which the difference between the just intervals represented by two notes is different from the interval represented by their difference. Effectively, it is the condition wherein an interval is legal in a precovergence web, but illegal in the convergence web.

Example:

Intervallic paradox describes the state of an interval being legal in a preconvergence but illegal in a convergence. It appears to make sense intervallically because it cross-rounds locally, but harmonically, the math is incorrect.

The ratio between the minor and major second, describing the "opening" of the minor second from non-existant in 5-tone, to the equi-diatonic of 7-tone.

(reference: stern brocot tree)

The second is defined as 9,192,631,770 ticks of a Cesium atom, which is used in atomic clocks. Orphon Soul uses this as the pulse grid of the universe and bases all tunings and tempos on this 9GHz frequency.

Since Orphon Soul also uses D as a tone center, the D string on a guitar is always tuned to 136.98Hz, 24 octaves below the Cesium tick. Strangely enough, in 19, 22, 41, 60, 63, etc this tuning yields a note very close to 440Hz.

The root, or "D" tempo is 128.42 beats per minute, 32 octaves below the tick.

Equalization, sample durations, and synthesizer timings are also considered.

Orphon Soul projects use D, not C, as a root for calculating scale values, used because of the symmetry:

[scalar order:]        A B C ((D)) E F G: D is the center.

[chain-of-4ths order:] B E A ((D)) G C F: D is the center.

[with accidentals:]    B# E# A# ((D#)) G# C# F#
                       B  E  A  ((D))  G  C  F
                       Bb Eb Ab ((Db)) Gb Cb Fb

                       etc...
				

This is used to easily calculate interval names and their inversions, so as to not have to constantly bargain with the off-balance accidentals.

A term suggested by Fred Freeburg, circa 1990, equivalent to equal temperament, ED2, tET, EDO etc. originally in lieu of the fact that Marc Jones uses so many equal temperaments. After Fred being handed new fretboards all the time, the routine arose, "oh, what Jones is this now? 12 Jones per octave? 19 Jones?" instead of "tones".

Later renewed in lieu of the discovery of Marc’s multiplicity, in that instead of trying to remember who each persona is and which temperament they relate to, omniously enough by the coining, it would be easier to remember them as "17 Jones", "19 Jones", etc.

Originally abbreviated J. Also Js or Jz, parodying Hertz (Hz). Also taken as the rebus, Jones = J + one + s, "J1s". With JI as an abbrev for "just intontation", this could look a bit like "just ones"

12-tET. 12-EDO. 12-ED2. 12-J. 12 Jz. 12 Js. 12 J1s.

Among Orphon Soul peers, Jz was always the favorite.

A multimicrotonal technique used as a slight chorusing effect to encourage and demystify practice and recording in a targeted scale class in a targeted temperament on guitar. This is broken into two parts: one nicknamed “shish kebab”*, because in the final mix you keep everything you put in, with an emphasis on the target, and “Chateaubriand”*, named after the steak dish in which two flank steaks are discarded after being used to cook the main steak; similarly, the cushions are discarded yielding the target. This is a bit like using “pads”, vocal pads, synth pads, etc, only temperament based.

* - It is a common practice at Orphon Soul to have FOOD nicknames for production techniques, related to the final preparation of music for consumption.

The conducive form of convergent cushioning.

Given A + B = C, where C is the target temperament and A + B is the scale class, the "cradling" effect would be by recording: Playing the A + C scale in (2A + B), Overdubbing the B + C scale in (A + 2B).

Example:

The inducive form of convergent cushioning.

Given A + B = C, where C is the target temperament and A + B is the scale class, the "stacking" effect would be by recording: Playing the A + (B - A) scale in B, Playing the (2A - B) + (B - A) scale in A .. etc.

There’s not a set pattern here. This can be more exploratory, not knowing what temperament you want to add back;

Example:

This version of stacking is called "climbing the tree", that is, the diatonic scale tree, when the temperaments stacked are moving directly up the tree.

All other stacking has no specific name although references have been made to monkeys, jumping around trees from branch to branch: Say building up 19 to 22 to 41 to 63. This would usually move up one level at a time, although not necessarily, and in this case, hardly straight up. In playing 19 to 27 to 46, 27 and 46 are on the same tree level. Or 32 to 39 to 71, 32 is actually on a higher level than 39.

The inducive form of divergent cushioning.

This is where chorusing effects take the most drastic shape. This involves creating a discrete network of temperaments wherein there is at least one noticeable occurance of a temperament not being able to cross-round to another temperament without first rounding through a third temperament.

Example:

The conducive form of divergent cushioning.

This just encourages you to play something different by targeting scales that aren’t cross-rounding in the first place. This is the most free cushioning, basically playing "whatever" so that you can then play your targeted "whatever."

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