Interesting, this Gil Trythall piece is the tune in the Commodore C-64 game "Thing on a Spring", isn't it. I didn't know that was a pre-existing piece.
Presumably it is an equal ratio like a piano keyboard, but with the 31st root of 2 as the ratio between successive frequencies instead of the 12th root of 2. Simple frequency ratios like 3/2 tend to sound good (this is commonly attributed to Pythagoras), so tunings are chosen to include them or close approximations.
Notice how there is one very close to 1.5 = 3/2, one very close to 1.3333... = 4/3, and one sort of close to 1.25 = 5/4. These intervals are the 5th, 4th, and major 3rd, and sound good. That's the main reason we use 12 semitones per octave.
There is still one very close to 1.5 = 3/2, one kind of close to 1.3333... = 4/3, one close to 1.25 = 5/4, and additionally one close to 1.2 = 6/5, one pretty close to 1.1666... = 7/6, one close to 1.1428... = 8/7, and one close to 1.111... = 10/9. More consonant intervals are possible with this keyboard than with standard notes, but they will sound strange and unfamiliar.
Personally, I don't find 31-TET compelling since it gives worse ratios for perfect fifths 3/2 (1.495 instead of 1.498) and thus perfect fourths 4/3 (1.337 instead of 1.335).
Anyway, back to 12-TET. Here's a useful formatting:
1.00 C = 1/1 unison, [diminished second]
1.06 C#/Db (augmented unison), minor second
1.12 D ~ 9/8 major second, [diminished third]
1.19 D#/Eb ~ 6/5 (augmented second), minor third
1.26 E ~ 5/4 major third, [diminished fourth]
1.33 F ~ 4/3 perfect fourth, [augmented third]
1.41 F#/Gb !!!!! satanic tritone (augmented fourth, diminished fifth)
1.50 G ~ 3/2 perfect fifth, [diminished sixth]
1.59 G#/Ab ~ 8/5 (augmented fifth), minor sixth
1.69 A ~ 5/3 major sixth, [diminished seventh]
1.78 A#/Bb ~16/9 (augmented sixth), minor seventh
1.89 B major seventh, [diminished octave]
2.00 C = 2/1 octave, [augmented seventh]
Note that intervals are named based on the natural version (i.e. considering only letter half), then modified for the accidentals (sharps and flats). The names in (parentheses) are somewhat less likely to be used of each pair (That is, C to D# is an augmented second, but C to Eb is the minor third and much more common). The names in [brackets] would also refer to the same interval ratio but require either a double accidental on one end, or a sharp and flat in different directions, neither of which I wrote out here. "Doubly/triply/quadruply diminished/augmented" are also possible prefixes but increasingly rare; I don't think further is possible when you're limited to double accidentals.
My brother couldn't produce the sound of a bassoon with an actual bassoon. Then again, I couldn't reproduce the sound of an oboe with an actual oboe. We both went back to our respective saxophones.
I'd like to offer a couple of thought from an eye-witness observation of this synth in 1969. It was quite a thrill to see this article. I had often wondered what happened to the instrument, if it was a one-off special, or if it was an item Moog produced in some quantity. That seemed unlikely as I had not seen or heard anything of it again until now and I was at least slightly aware of the Moog products from their literature and commercial use.
I can't remember how I was introduced to David Rothenberg. I had an interest in electronic music then (and now) and, while far from an active participant, I did have some communications with others in the field. Perhaps one of them made the introduction. I'm also not sure why I contacted him. It may have been just curiosity but more likely I was hoping to work with him as I believe that we discussed that possibility though I vaguely think he was looking for a volunteer. Whatever the source and purpose I have a vivid recollection of meeting him, the inside of his studio/lab, and, of course, this synthesizer.
I found an entry in my notebook from the time at a point in the book that implies I made the entry in 1969. The note includes David's name and an address on West 113th Street in Manhattan, which is where I suspect I met him. I remember only one floor of the building, a studio or lab, quite spartan, just white walls, and two components of the synth - the keyboard, and the electronics modules. I can remember nothing indicating it was also his residence though this would be plausible or it might just have been his place of business.
The keyboard - from seeing it in person and from my conversation with David my recollection is that he wanted to explore micro-tonality, that is, intervals smaller than a semitone. My recollection of the keyboard differs a bit from what is shown in the video here. After 54 years it is entirely plausible that my memory is hazy but I also wonder if the keys in the restoration are not original. I don't remember the gray keys. What I remember is an ordinary piano-type keyboard - one row of white keys & black keys in the usual horizontal configuration and with the standard pitches of the chromatic scale. But then, this horizontal row was reproduced many times vertically, that is, moving from front to back. The video here shows eleven rows total but I have no recollection of the actual count, just that there were many. The pitch of each of the rows was offset slightly from the one below it to obtain the micro-tonal spacing. Playing horizontally on any one row of keys would produce the same pitch intervals as a piano. But playing vertically (front to back) would produce micro-tonal intervals. While I have no recollection to support this I suspect that the interval going up would be a semitone divided by the number of rows on a logarithmic scale. That is, for eleven rows the vertical spacing would be the (11*12)th root of 2. I find it a bit strange that there are eleven rows and not twelve as twelve would make it symmetric with a spacing of the 144th root of 2. No matter, the video shows eleven rows and I have no recollection to dispute that.
The electronics - here I'm less clear but I have an image of a tall wooden box, much like a grandfather clock, with many rows of electronic circuit boards, which I presume were the oscillators, filters, envelope generators, etc. I have absolutely no memory of any sort of control panel of the type seen on commercial Moog (or other) synths with lots of pots and patch cords. And this memory is very specifically not of a standard metal 19" electronics rack but something smaller and made of wood. There would have to have been some mechanism for controlling the electronics, perhaps some controls above the keyboard, but I cannot recall it.
Well, that's my story of a brief meeting with David Rothenberg 54 years ago. I might not know what I had for breakfast today but the studio, keyboard, and electronics are still vivid in my mind. I'm glad to learn that the keyboard survived, where it has been all these years, and now that it has been restored.
I gave the year 1969 only because of the position of David's address in my notebook, not because of any documentation containing a date. Based on my work at the time it is entirely possible that the visit occurred in 1970 or even later. I mention this to address the possibility that the year 1969 does not align with other elements of the story.
Readit News
https://www.discogs.com/master/331353-Gil-Trythall-Switched-...
The other ones are atypical for Country (no cowboys in sight)
https://www.youtube.com/watch?v=nGIUtLO_x8g&pp=ygUWbWluZCB5b...
https://www.youtube.com/watch?v=GZfj2Ir3GgQ&pp=ygUea2FjZXkgb...
https://www.youtube.com/watch?v=AeRP8rQ-07Ihttps://www.youtube.com/watch?v=QhkFF0c-gUo
The relative frequencies for a piano octave are:
Notice how there is one very close to 1.5 = 3/2, one very close to 1.3333... = 4/3, and one sort of close to 1.25 = 5/4. These intervals are the 5th, 4th, and major 3rd, and sound good. That's the main reason we use 12 semitones per octave.Relative frequencies for 31 divisions are:
There is still one very close to 1.5 = 3/2, one kind of close to 1.3333... = 4/3, one close to 1.25 = 5/4, and additionally one close to 1.2 = 6/5, one pretty close to 1.1666... = 7/6, one close to 1.1428... = 8/7, and one close to 1.111... = 10/9. More consonant intervals are possible with this keyboard than with standard notes, but they will sound strange and unfamiliar.More info here: https://en.wikipedia.org/wiki/31_equal_temperament and https://en.wikipedia.org/wiki/Regular_temperament
Anyway, back to 12-TET. Here's a useful formatting:
Note that intervals are named based on the natural version (i.e. considering only letter half), then modified for the accidentals (sharps and flats). The names in (parentheses) are somewhat less likely to be used of each pair (That is, C to D# is an augmented second, but C to Eb is the minor third and much more common). The names in [brackets] would also refer to the same interval ratio but require either a double accidental on one end, or a sharp and flat in different directions, neither of which I wrote out here. "Doubly/triply/quadruply diminished/augmented" are also possible prefixes but increasingly rare; I don't think further is possible when you're limited to double accidentals.Deleted Comment
For examples of people playing them, search for Lumatone on YouTube, or “microtonal”, or “xenharmonic”.
I can't remember how I was introduced to David Rothenberg. I had an interest in electronic music then (and now) and, while far from an active participant, I did have some communications with others in the field. Perhaps one of them made the introduction. I'm also not sure why I contacted him. It may have been just curiosity but more likely I was hoping to work with him as I believe that we discussed that possibility though I vaguely think he was looking for a volunteer. Whatever the source and purpose I have a vivid recollection of meeting him, the inside of his studio/lab, and, of course, this synthesizer.
I found an entry in my notebook from the time at a point in the book that implies I made the entry in 1969. The note includes David's name and an address on West 113th Street in Manhattan, which is where I suspect I met him. I remember only one floor of the building, a studio or lab, quite spartan, just white walls, and two components of the synth - the keyboard, and the electronics modules. I can remember nothing indicating it was also his residence though this would be plausible or it might just have been his place of business.
The keyboard - from seeing it in person and from my conversation with David my recollection is that he wanted to explore micro-tonality, that is, intervals smaller than a semitone. My recollection of the keyboard differs a bit from what is shown in the video here. After 54 years it is entirely plausible that my memory is hazy but I also wonder if the keys in the restoration are not original. I don't remember the gray keys. What I remember is an ordinary piano-type keyboard - one row of white keys & black keys in the usual horizontal configuration and with the standard pitches of the chromatic scale. But then, this horizontal row was reproduced many times vertically, that is, moving from front to back. The video here shows eleven rows total but I have no recollection of the actual count, just that there were many. The pitch of each of the rows was offset slightly from the one below it to obtain the micro-tonal spacing. Playing horizontally on any one row of keys would produce the same pitch intervals as a piano. But playing vertically (front to back) would produce micro-tonal intervals. While I have no recollection to support this I suspect that the interval going up would be a semitone divided by the number of rows on a logarithmic scale. That is, for eleven rows the vertical spacing would be the (11*12)th root of 2. I find it a bit strange that there are eleven rows and not twelve as twelve would make it symmetric with a spacing of the 144th root of 2. No matter, the video shows eleven rows and I have no recollection to dispute that.
The electronics - here I'm less clear but I have an image of a tall wooden box, much like a grandfather clock, with many rows of electronic circuit boards, which I presume were the oscillators, filters, envelope generators, etc. I have absolutely no memory of any sort of control panel of the type seen on commercial Moog (or other) synths with lots of pots and patch cords. And this memory is very specifically not of a standard metal 19" electronics rack but something smaller and made of wood. There would have to have been some mechanism for controlling the electronics, perhaps some controls above the keyboard, but I cannot recall it.
Well, that's my story of a brief meeting with David Rothenberg 54 years ago. I might not know what I had for breakfast today but the studio, keyboard, and electronics are still vivid in my mind. I'm glad to learn that the keyboard survived, where it has been all these years, and now that it has been restored.
I gave the year 1969 only because of the position of David's address in my notebook, not because of any documentation containing a date. Based on my work at the time it is entirely possible that the visit occurred in 1970 or even later. I mention this to address the possibility that the year 1969 does not align with other elements of the story.