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Collection Notes:

The point of this collection is to explore the possibilities of natural and microtonal tunings (as opposed to the tempered scale of twelve geometrically proportioned semitones). So if you are willing, spin up TRACK 6 and you'll hear some tones and harmonies that are a bit different than what one usually hears on adult contemporary radio stations circa 2008.

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Above is the short story. What follows is the longer version.

When I was younger, I was curious about the relationships between the pitches of the major and minor scales. Thinking it had something to do with the geometrically proportioned pitches of the chromatic scale, I threw myself into the study of logarithms. But it turned out that the natural major scale is based on simple ratios between the frequencies of the pitches and the resulting pitches just happen by coincidence to approximate those in the tempered chromatic scale.

For instance, let's say that our middle C is 264 Hz. By multiplying this frequency by 4, 5, and 6 we get the notes C, E, and G of the C Major triad. Take that G and multiply it by 4, 5, and 6 and we will get G, B, and D of the G Major triad. Go back to the C and divide it by 3. That gives us an F. Then multiply the frequency of F by 4, 5, and 6 to give us F, A, and C of the F Major triad. Arranging these notes in order (after adjusting to keep them within an octave) gives us the C Major Natural Scale:

 do  C  264 Hz             
 re  D  297 Hz = 264 X 9/8 
 mi  E  330 Hz = 264 X 5/4 
 fa  F  352 Hz = 264 X 4/3 
 so  G  396 Hz = 264 X 3/2 
 la  A  440 Hz = 264 X 5/3 
 ti  B  495 Hz = 264 x 15/8
 do  C  528 Hz = 264 X 2   

The above C Major natural scale uses the pitches of the C Major triad (I), the F Major triad (IV), and the G Major triad (V) arranged in order. In natural scales such as this one, the frequencies of the pitches are in very simple ratios with one another. (By the way, to convert this natural C Major scale to the relative natural A minor scale, the D needs to be adjusted to 264 X 10/9 = 293.333 Hz. Natural minor scales are based on multiples of the wavelength (such as the length of the pipes in a pan pipe) whereas natural Major scales are based on the harmonic series (multiples of the tonic frequency). The minor scale is the "relative inverse" of the Major scale.)

The problem with natural scales is that it is difficult to modulate from one key to another. The farther we get away from our home key, the more out of tune we are. And that is why JS Bach (and everyone else) embraced tempered tunings: the scales are slightly out of tune when strictly compared to natural scales, but they do not get any worse as one modulates away from the home key. Bach liked his "Well-Tempered Clavier" so much he wrote several cycles of pieces for it. (The clavier of Bach's day was an interesting hybrid of a stringed instrument and a keyboard. I wish they still sold them in music stores!)

   Natural   Tempered          
   -------   --------          
 C  264 Hz   261.626           
             277.183  C#/D flat
 D  297 Hz   293.664           
             311.127  D#/E flat
 E  330 Hz   329.628           
 F  352 Hz   349.228           
             369.994  F#/G flat
 G  396 Hz   391.995           
             415.305  G#/A flat
 A  440 Hz   440               
             466.164  A#/B flat
 B  495 Hz   493.883           
 C  528 Hz   523.251           

In the tempered chromatic scale, each pitch is different from the adjacent pitch by a factor of the twelfth root of two or 1.0594630943592952645618252949463 (if you have a fancy handheld calculator, take the square root of 2 twice, then find the cube root of that). The A above middle C is arbitrarily defined as 440 Hz and all the other pitches are computed from that.

Another question comes to mind: Can musical systems be constructed that use pitches OTHER than the ones approximated by the twelve semitones of the tempered scale? Answer: Sure, why not? The major natural scale just described uses pitches with frequencies in ratios with one another of multiples of 2, 3, and 5. If one gets a bit creative one can extend the ratios to include multiples of 7, 11, and 13 as well (but it is not all that easy).

After exploring the mathematical relationships between pitches of various scales and harmonies, I became anxious to physically hear the things I had been writing on paper. That is when I found it necessary to develop my own computer program that could construct sound waves of any desired pitch in a variety of different voicings. The result was a computer program I called "NEW WAVE."

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01.) The Hammer That Killed John Henry

This tune has nothing to do with NEW WAVE. I had just recently bought some brand new microphones and I was anxious to try them out. Besides, this supplies a good title for the collection.

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02.) JS Bach: Little Fugue in G minor

Bach would roll over in his grave, but this track was put together using NEW WAVE and all natural scales. Fortunately when Bach modulated from key to key in this piece, he retraced his steps back to the home key making it possible for me to switch from natural scale to natural scale and back again.

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03.) HIWAY#9

Here's a tune I put together with NEW WAVE featuring pitches that are multiples of 7 and 11 to extend the range of the traditional natural scale.

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04.) Boötes

This NEW WAVE tune is mainly based on pitches of the natural harmonic series (1 through 19) played against drones of the tonic and the fifth. Many of these pitches are not represented in the natural major scale. Boötes is pronounced boo-OAT-eez and is the constellation of the goat herder in the northern sky.

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05.) original ChiveJam

What's up with the blues? Why do blues artists use the pitches they use? Why do they use the flatted seventh and the flatted third (and sometimes even a diminished fifth!) against the major scale? Here I'm exploring those issues with natural scales extended by adding pitches that are multiples of seven. This gives us a "flatted seventh", for instance, that is quite a bit "flatter" than the flatted seventh of the tempered scale and also a "flatted third" (seven times the fourth degree of the scale) that is quite a bit "flatter" as well. Believe it or not the more I listen to this track, the more "natural" it sounds.

If the sounds of these natural scales are a bit much for you, go to the last track in this collection and listen to Tempered ChiveJam. This is the exact same tune except it uses tempered scales.

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06.) Power Surge

...yet another experiment with non-standard tunings.

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07.) JS Bach: Tocatta and Fugue in D minor

This tune was put together using tempered scales just like Bach would have wanted. I tried, but I found it impossible to reinterpret this piece with natural scales as Bach leaves the home key going in one direction and returns to the home key via a different route.

[NOTE: Sometime later I went back and tried again to reinterpret this piece using all natural scales. The surviving audio track included in this collection is, for better or worse, the end result. --MJH January 2019]

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08.) Branch of Jesse

I want to be a composer so bad, I can hardly stand it! But since I can't play keyboards my options are a bit limited. A commercially available software product called Melody Assistant (www.myriad-online.com) was used to put this track together.

"Branch of Jesse" was inspired by "Lo, A Rose Electric", a piece that I arranged for Melody Assistant that was adapted from the traditional tune, "Lo, A Rose E'er Blooming" (I really liked the way that piece turned out). In "Branch of Jesse" the main theme (in a major key) is interrupted before it plays out by a restatement of the theme in a minor key. Then the theme is presented in the inverted minor key (which turns out to be major), next presented in the inverted major key (which turns out to be minor), and finally the original main theme is presented in its entirety (the first time the whole original main theme plays out from beginning to end). Lots of other stuff goes on in between times. This piece took me two solid years to write (2006-2008), the longest I've ever continuously worked on anything.

I kinda imagine "Branch of Jesse" to be my interpretation of Christ's gift of redemption in a world that was (and is) broken by sin.

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09.) Le Pickup Marche

This is Zydeco music at it's finest! I was inspired by a Mardi Gras Cajun Festival held at Iowa's Amana Colonies - the only place that I know of where one can hear an African-American man playing the accordion and singing in French in a region settled by a religious German colony. I originally composed this piece on Melody Assistant but later re-did it with natural scales using New Wave.

I call this piece "Le Pickup Marche" (literally, "the record player works") because it's one of the few French phrases I know.

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JS Bach on His Head (Little Fugue Inverted)

Back in 2005 I was working on inverting JS Bach's Little Fugue in G minor (I was using my own "Synth-Wave" digitizing program at the time instead of "New-Wave.") So what is inversion? Well, whenever the original melody goes up a perfect fifth the inverted version goes down a perfect fifth. Whenever the original melody goes down a minor third the inverted version goes up a minor third. And et cetera. Not only that; the highest register becomes the pedal tones and the pedal tones become the highest register.

I promptly lost this piece and forgot about it because I got involved in a different project. Then very early in 2021 when I was digging through my digital trash barrel I came across this again and re-digitized it using "New-Wave."

Interesting, but does it work?

Yeah, it kinda works! Bach's upper register was never intended to be the pedal tones but despite that it's kinda fun to listen to it. You be the judge.