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1. Mohajira improv

Mohajira improv

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2. A Porcupine Comma Pump - 22-EDO version

A Porcupine Comma Pump - 22-EDO version

This is a comma pump in porcupine which goes up by three 6/5's and then down two 4/3's back to 1/1. I designed it as an example of something that I thought sounded perfectly "natural," but which doesn't work at all in 12-EDO. I'll use this in a piece somewhere down the road. The tuning here is 22-EDO.

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3. Tonality, Patterns in 11-EDO

Tonality, Patterns in 11-EDO

Phases of this example - 1) starts off in orgone[11], LLsLsLs mode, moves around by half step within that mode 2) abandons the MOS in order to obtain more consonant harmony, shifts the base chord from 7:9:11 to 4:7:9:11 3) once you have some basic "resolution," whatever it is, just go crazy and use it everywhere, setting the tonality up in a bunch of disparate keys, a la Bach. Of course, since we hate 12, we won't do it by rotating around the meantone circle of fifths - in this case we'll do a 5625/5488 comma pump instead

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4. Bach - Fugue in C Major (BWV952) - 31-EDO

Bach - Fugue in C Major (BWV952) - 31-EDO

In this set of listening examples, common practice works have been retuned to exotic tunings in which the relative structure of the diatonic scale is always preserved, so that it always takes the form of LLsLLLs (for "Large step" and "small step," respectively). The perfect fifth, which generates the scale, is allowed to vary from as flat as 7-EDO, where the diatonic scale is a perfectly evened-out "neutral" diatonic scale, to as sharp as 5-EDO, where the half step becomes so small that it vanishes, leaving a perfectly evened-out pentatonic scale. The chosen spectrum of tunings is such that diatonic interval categories such as the "major third" may, at times, approximate different intervals from the harmonic series than they normally would in 12 equal temperament, just as long as the LLsLLLs scale pattern is consistently present in the tuning. These experiments aim to explore the properties of the "categorical perception" effect, and to see to what extent it exists and interrelates with the missing fundamental phenomenon and other psychoacoustic effects. The "artwork" for this compilation describes the tunings used, and the properties of each one; click "Download Artwork" to view it. In this particular set, the chosen composition is Bach's Fugue in C Major (BWV952).

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5. 60x60 Porcupine Fragment

60x60 Porcupine Fragment

This piece is in porcupine temperament and almost surely just a small part of a larger thing. 22-EDO is the tuning.

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6. A Porcupine Comma Pump - 37-EDO version

A Porcupine Comma Pump - 37-EDO version

This is a comma pump in porcupine which goes up by three 6/5's and then down two 4/3's back to 1/1. I designed it as an example of something that I thought sounded perfectly "natural," but which doesn't work at all in 12-EDO. I'll use this in a piece somewhere down the road. The tuning here is 37-EDO.

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7. The Mavila Experiments - Beethoven - Fur Elise - 16-EDO

The Mavila Experiments - Beethoven - Fur Elise - 16-EDO

==16-EDO VERSION== These musical examples are tuned to what is known as "mavila" temperament. It is named after the Mavila village of the Chopi people in southern Mozambique, where this tuning system was first discovered by Kraig Grady. Because of the structure of this unique tuning, it is true that every existing piece of common practice music has a "shadow" version in mavila temperament. That is, when Beethoven wrote Fur Elise, he actually wrote two compositions - the one that you know, and the anti-diatonic equivalent in mavila temperament. It's only that the anti-diatonic versions have never been heard before. Mavila is a tuning system whereby four stacked perfect fifths, rather than getting you to a major third, gets you to a minor third - meaning that the fifths are flat. Conversely, four stacked perfect fourths gets you to a major third, rather than a minor third. This has some very strange implications for music. The mavila diatonic scale is similar to the normal diatonic scale - except interval classes are flipped. Wherever there was a major third, you'll find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major - you end up with three parallel natural/harmonic/melodic major scales, and only one minor scale. Instead of a diminished triad in the major scale, there is now an augmented triad. In these examples, the chosen mavila temperament is 16-equal, which was chosen because it strikes a good middle ground between approximating the harmonic series and making the interval categories as distinct as possible. In contrast, 23-equal improves the fit of this temperament to the harmonic series, whereas 25-equal makes the intervals more distinct from one another. A special thanks goes out to Graham Breed; his custom Lilypond code and several weeks worth of gchat discussion are what made all of this possible.

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8. Functional Harmony in Porcupine Temperament, Excerpt (15-tet version)

Functional Harmony in Porcupine Temperament, Excerpt (15-tet version)

This is an excerpt that aims to take advantage of the 250/243 unison vector of porcupine temperament. 15-tet is the tuning here.

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9. Bach - Fugue in C Major (BWV952) - 40-EDO

Bach - Fugue in C Major (BWV952) - 40-EDO

In this set of listening examples, common practice works have been retuned to exotic tunings in which the relative structure of the diatonic scale is always preserved, so that it always takes the form of LLsLLLs (for "Large step" and "small step," respectively). The perfect fifth, which generates the scale, is allowed to vary from as flat as 7-EDO, where the diatonic scale is a perfectly evened-out "neutral" diatonic scale, to as sharp as 5-EDO, where the half step becomes so small that it vanishes, leaving a perfectly evened-out pentatonic scale. The chosen spectrum of tunings is such that diatonic interval categories such as the "major third" may, at times, approximate different intervals from the harmonic series than they normally would in 12 equal temperament, just as long as the LLsLLLs scale pattern is consistently present in the tuning. These experiments aim to explore the properties of the "categorical perception" effect, and to see to what extent it exists and interrelates with the missing fundamental phenomenon and other psychoacoustic effects. The "artwork" for this compilation describes the tunings used, and the properties of each one; click "Download Artwork" to view it. In this particular set, the chosen composition is Bach's Fugue in C Major (BWV952).

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10. 17496/16807 Comma Pump, Minor Chords, 34-equal

17496/16807 Comma Pump, Minor Chords, 34-equal

This is a comma pump in the unnamed 17496/16807 temperament, tuned to 34-equal. Although the basic root movement is by 7/6, the chords are tuned to 5-limit minor 7 chords, to make them brighter.

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11. The Mavila Experiments - Beethoven - Moonlight Sonata - 23-EDO

The Mavila Experiments - Beethoven - Moonlight Sonata - 23-EDO

These musical examples are tuned to what is known as "mavila" temperament. It is named after the Mavila village of the Chopi people in southern Mozambique, where this tuning system was first discovered by Kraig Grady. By virtue of the structure of this unique tuning, every existing piece of common practice music has a "shadow" equivalent rendition in mavila. That is, when Bach wrote Fur Elise, he actually wrote two songs - the one that you know, and the anti-diatonic equivalent in mavila temperament. It's only that the anti-diatonic versions have never been heard before. Mavila is a tuning system whereby four stacked perfect fifths, rather than getting you to a major third, gets you to a minor third - meaning that the fifths are flat. Conversely, four stacked perfect fourths gets you to a major third, rather than a minor third. This has some very strange implications for music. The mavila diatonic scale is similar to the normal diatonic scale - except interval classes are flipped. Wherever there was a major third, you'll find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major - you end up with three parallel natural/harmonic/melodic major scales, and only one minor scale. Instead of a diminished triad in the major scale, there is now an augmented triad. In these examples, the chosen mavila temperament is 23-equal, which was chosen to provide greater accuracy in approximating the harmonic series. 16-equal is another good choice, with 9-equal also being good enough for government work.

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12. A Porcupine Comma Pump - 23-EDO version

A Porcupine Comma Pump - 23-EDO version

This is a comma pump in porcupine which goes up by three 6/5's and then down two 4/3's back to 1/1. I designed it as an example of something that I thought sounded perfectly "natural," but which doesn't work at all in 12-EDO. I'll use this in a piece somewhere down the road. The tuning here is 23-EDO, which does a much poorer job in approximating the harmonic series when compared to the other tunings listed here, so the chords don't seem to blend as well. That notwithstanding, it still has a certain interesting color to it, which I somewhat enjoy.

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13. Bach - Fugue in C Major (BWV952) - 19-EDO

Bach - Fugue in C Major (BWV952) - 19-EDO

In this set of listening examples, common practice works have been retuned to exotic tunings in which the relative structure of the diatonic scale is always preserved, so that it always takes the form of LLsLLLs (for "Large step" and "small step," respectively). The perfect fifth, which generates the scale, is allowed to vary from as flat as 7-EDO, where the diatonic scale is a perfectly evened-out "neutral" diatonic scale, to as sharp as 5-EDO, where the half step becomes so small that it vanishes, leaving a perfectly evened-out pentatonic scale. The chosen spectrum of tunings is such that diatonic interval categories such as the "major third" may, at times, approximate different intervals from the harmonic series than they normally would in 12 equal temperament, just as long as the LLsLLLs scale pattern is consistently present in the tuning. These experiments aim to explore the properties of the "categorical perception" effect, and to see to what extent it exists and interrelates with the missing fundamental phenomenon and other psychoacoustic effects. The "artwork" for this compilation describes the tunings used, and the properties of each one; click "Download Artwork" to view it. In this particular set, the chosen composition is Bach's Fugue in C Major (BWV952).

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14. The Mavila Experiments - Beethoven - Fur Elise - 25-EDO

The Mavila Experiments - Beethoven - Fur Elise - 25-EDO

These musical examples are tuned to what is known as "mavila" temperament. It is named after the Mavila village of the Chopi people in southern Mozambique, where this tuning system was first discovered by Kraig Grady. By virtue of the structure of this unique tuning, every existing piece of common practice music has a "shadow" equivalent rendition in mavila. That is, when Bach wrote Fur Elise, he actually wrote two songs - the one that you know, and the anti-diatonic equivalent in mavila temperament. It's only that the anti-diatonic versions have never been heard before. Mavila is a tuning system whereby four stacked perfect fifths, rather than getting you to a major third, gets you to a minor third - meaning that the fifths are flat. Conversely, four stacked perfect fourths gets you to a major third, rather than a minor third. This has some very strange implications for music. The mavila diatonic scale is similar to the normal diatonic scale - except interval classes are flipped. Wherever there was a major third, you'll find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major - you end up with three parallel natural/harmonic/melodic major scales, and only one minor scale. Instead of a diminished triad in the major scale, there is now an augmented triad. In these examples, the chosen mavila temperament is 25-equal, which was chosen so as to make all of the intervals in the mavila anti-diatonic scale to be as "distinct" from one another as possible, albeit at the sake of accuracy in approximating the harmonic series. 23-equal gains harmonic accuracy at the cost of categorical clarity, and 16-equal mediates between the two.

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15. The Mavila Experiments - Beethoven - Fur Elise - 9-EDO

The Mavila Experiments - Beethoven - Fur Elise - 9-EDO

==CRAZY 9-EDO VERSION - FOR USE ONLY IF YOU'RE TRAPPED ON A DESERT ISLAND WITH ONLY ONE INSTRUMENT IN 9-EDO== These musical examples are tuned to what is known as "mavila" temperament. It is named after the Mavila village of the Chopi people in southern Mozambique, where this tuning system was first discovered by Kraig Grady. Because of the structure of this unique tuning, it is true that every existing piece of common practice music has a "shadow" version in mavila temperament. That is, when Beethoven wrote Fur Elise, he actually wrote two compositions - the one that you know, and the anti-diatonic equivalent in mavila temperament. It's only that the anti-diatonic versions have never been heard before. Mavila is a tuning system whereby four stacked perfect fifths, rather than getting you to a major third, gets you to a minor third - meaning that the fifths are flat. Conversely, four stacked perfect fourths gets you to a major third, rather than a minor third. This has some very strange implications for music. The mavila diatonic scale is similar to the normal diatonic scale - except interval classes are flipped. Wherever there was a major third, you'll find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major - you end up with three parallel natural/harmonic/melodic major scales, and only one minor scale. Instead of a diminished triad in the major scale, there is now an augmented triad. In these examples, the chosen mavila temperament is 9-equal, which was chosen because there are only 9 notes to the octave. It's an odd tuning, in that although it has comparatively awful harmonic properties, and its melodic properties are a mixed bag, it does "work" in a sense: it's a rare novelty that allows you to set up tonality with only 9 notes to the octave. If you plan on getting stuck on a desert island sometime soon, and you only have 9 pieces of wood with which to construct a 9-tone wooden xylophone, it would be worthwhile to know how to use this tuning. A special thanks goes out to Graham Breed; his custom Lilypond code and several weeks worth of gchat discussion are what made all of this possible.

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16. The Mavila Experiments - Bach - Invention #8 - 25-EDO

The Mavila Experiments - Bach - Invention #8 - 25-EDO

These musical examples are tuned to what is known as "mavila" temperament. It is named after the Mavila village of the Chopi people in southern Mozambique, where this tuning system was first discovered by Kraig Grady. By virtue of the structure of this unique tuning, every existing piece of common practice music has a "shadow" equivalent rendition in mavila. That is, when Bach wrote Fur Elise, he actually wrote two songs - the one that you know, and the anti-diatonic equivalent in mavila temperament. It's only that the anti-diatonic versions have never been heard before. Mavila is a tuning system whereby four stacked perfect fifths, rather than getting you to a major third, gets you to a minor third - meaning that the fifths are flat. Conversely, four stacked perfect fourths gets you to a major third, rather than a minor third. This has some very strange implications for music. The mavila diatonic scale is similar to the normal diatonic scale - except interval classes are flipped. Wherever there was a major third, you'll find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major - you end up with three parallel natural/harmonic/melodic major scales, and only one minor scale. Instead of a diminished triad in the major scale, there is now an augmented triad. In these examples, the chosen mavila temperament is 25-equal, which was chosen so as to make all of the intervals in the mavila anti-diatonic scale to be as "distinct" from one another as possible, albeit at the sake of accuracy in approximating the harmonic series. 23-equal gains harmonic accuracy at the cost of categorical clarity, and 16-equal mediates between the two.

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17. Bach - Fugue in C Major (BWV952) - 27-EDO

Bach - Fugue in C Major (BWV952) - 27-EDO

In this set of listening examples, common practice works have been retuned to exotic tunings in which the relative structure of the diatonic scale is always preserved, so that it always takes the form of LLsLLLs (for "Large step" and "small step," respectively). The perfect fifth, which generates the scale, is allowed to vary from as flat as 7-EDO, where the diatonic scale is a perfectly evened-out "neutral" diatonic scale, to as sharp as 5-EDO, where the half step becomes so small that it vanishes, leaving a perfectly evened-out pentatonic scale. The chosen spectrum of tunings is such that diatonic interval categories such as the "major third" may, at times, approximate different intervals from the harmonic series than they normally would in 12 equal temperament, just as long as the LLsLLLs scale pattern is consistently present in the tuning. These experiments aim to explore the properties of the "categorical perception" effect, and to see to what extent it exists and interrelates with the missing fundamental phenomenon and other psychoacoustic effects. The "artwork" for this compilation describes the tunings used, and the properties of each one; click "Download Artwork" to view it. In this particular set, the chosen composition is Bach's Fugue in C Major (BWV952).

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18. Happy Birthday

Happy Birthday

This is a reharmonization of Happy Birthday, tuned to 22 equal divisions of the octave. It is loosely centered around what we call "porcupine temperament."

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19. Etude No. 1 in 17-tone Equal Temperament

Etude No. 1 in 17-tone Equal Temperament

This is a simple study in four-part harmony in 17-equal temperament. I predominantly used the diatonic scale, but also often used the 9-note "progression" scale which is found in 17-equal as well. I also broke away from scalar structures often, preferring to fill the space in with shifting 13-limit harmony when possible. More intense theory: I used the <17 27 40 48 59 63] val for 17-equal, meaning I treated it as though it supported meantone temperament rather than dicot temperament. Progression temperament can be found here: http://x31eq.com/cgi-bin/rt.cgi?ets=8_9&error=34.070&limit=13&invariant=5_3_7_4_6_1_1_2_2_3_3

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20. Functional Harmony in Porcupine Temperament, Higher-Limit Extensions

Functional Harmony in Porcupine Temperament, Higher-Limit Extensions

This is an "enriched" version of the original porcupine experiment. It is enriched by turning the major chords into higher-limit tetrads and pentads, in the same way that the blues or Gershwinian techniques enrich meantone. This is not a composition at all, but rather a technical experiment in classical "functional" harmony in other temperaments than meantone. In this case, I utilize some secondary dominants in porcupine temperament, which eliminates the 250/243 unison vector as opposed to meantone's 81/80. The basic chord progression is, in meantone notation - Cmaj -> A/C# -> Dmaj -> B/D# -> Emaj -> C#/E# -> F#maj -> F#m6 -> C#maj, except the whole thing is tempered such that the C#maj at the end is actually the same as the Cmaj that you started at. The first example changes many of the chords from 4:5:6 triads to 8:11:12. In addition, it changes the Fm6 (notated as F#m6 above) to a 3:4:5 under the D on top. The second example mimics the first, but adds some counterpoint sensibilities to the mix. The third example is an 11-limit shredfest that sticks loosely to the "porcupine hearing" that we've just established, but adds 11-limit extensions on top, similarly to how the blues functions over meantone.

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