Using Fractal Tune Smithy I retuned my Roland GR-20 to this tuning
116.129 387.097 425.806 696.774 812.903 1006.452 2/1
Which is named: Strange diatonic-like strictly proper scale
I then improvised finger picking on my Fender Mustang. Most everything I hit was ok sounding.
I think the improvisation came out ok if you ignore the noise and a couple missed notes.
Download: Strictly Proper Strange Diatonic
This is an improvisation around a few chords I found when experimenting with two simultaneous tunings on my Fender Mustang run through a Roland GR-20 re-tuned to Arabic 17 note Pythagorean tuning and mixing in my Mustang through my DoD FX-7 in 12 equal.
In Search of Perfect Consonance
The way this works is this:
1. The Roland GR-20 pick up (whatever name that has) has a plug to take the normal signal from the guitar and routes that down the 11 pin cable to the GR-20. The GR-20 then has a out for the normal guitar signal which I then route to my DoD FX-7 to apply some phase shift and from the DoD FX 7 back to the GR-20 in stereo.
2. The hexaphonic pick up from the GR-20 sends 6 analog signals (1 per string) to the GR-20. Each signal is converted to midi. This midi is sent to the computer sound card midi port on channels 1 through 6. FTS then adds pitch bends to re-tune the incoming midi to 17 tone Pythagorean and then sends the re-tuned midi back out the soundcard midi port.
3. The GR-20 is run in “local control off” mode which means the midi from the guitar conversion does not control the synthesizer but instead the re-tuned midi from FTS does. This generates a synthetic guitar which is pretty good sounding in the 17 Pythagorean tuning.
4. The two signals are combined (phase shifted guitar in 12 equal and synthesized guitar in 17 Pythagorean) with some volume balancing to give what you hear.
Download or listen to Bridgeport 2
Note: – this is best listened to at a volume as if you were close up front and center to a fairly powerful orchestra.
Story: In response the popularity of Michael Sheiman’s silver and phi tunings Michael Sheiman and Cameron Bobro joined forces to create a “Super Particular” tuning system for me to compose with. This piece is the first created with this tuning.
1/1 0.000 —– unison, perfect prime
13/12 138.573 —– tridecimal 2/3-tone
9/8 203.910 —– major whole tone
39/32 342.483 —– 39th harmonic, Zalzal wosta of
117/88 493.120
63/44 621.418
3/2 701.955 —– perfect fifth
25/16 772.627 —– classic augmented fifth
5/3 884.359 —– major sixth, BP sixth
16/9 996.090 —– Pythagorean minor seventh
24/13 1061.427 —– tridecimal neutral seventh
25/13 1132.100
2/1 1200.000 —– octave
The realization uses Sonar 8.5 and Garritan Personal Orchestra 4 (Aria player) and relies heavily on Sonar’s sequencing interface. The compositional method was the creation of a number of sequenced motives which were combined as needed with overlays of more traditionally composed portions.
A couple notes on the tuning:
From Michael
I found that tuning the middle C AKA 1/1 to about 75/76 * middle C = approximately 258hz realigns the tonal centers in such a way it works well for re-tuning 12TET pieces. I tried this with Beethoven’s “Drei Equeli” (sp.?) and it works well with about 90-95% of the notes. Makes me wonder just how pitch and perhaps alignment with the basilar membrane can skew perception of intervals as, of course, many of the intervals in the scale are very non-12TET like.
and
Super particular….to the best of my understanding that’s what Cameron used to fine-tune the scale. It includes reducing intervals between two tones to fractions like 21/20 and 15/14 AKA (n + 1)/n. As I understand it Cameron managed to make all dyads follow this format (and that’s how he came up with odd high-numbered fractions that, miraculously, sound better than the low numbered ones).
In general in the scale:
1) Close tones have more periodic consonance (due to super-particular format) but less critical band consonance
2) Far tones don’t match super-particular relationships perfectly (though they still get fairly close) so they lose some periodic consonance…but they are further apart and thus have more critical band consonance
This combination of the 2 types of consonance balances out so the average consonance of dyads both closer and further apart stays fairly similar…as opposed to 7-tone diatonic JI where closer tones/dyads (IE the 15/14 half-step so often avoided in common-practice chords) often have BOTH lower periodic consonance AND lower critical band consonance than ones further apart. It’s all about balance….
And from Cameron
The intervals between the scale steps were all superparticular (n+1/n) except those couple, so I just made the steps superparticular. Scales that are composed only of superparticular steps tend to be smooth and “as one” sounding, something noticed and applied thousands of years ago.
And in response to Michael’s last couple paragraphs
Yes that’s what superparticular means- n+1/n. It is the same as being adjacent partials in a harmonic series. Most of the ancient Greek theory tried to stick only to superparticular ratios. This isn’t numerology, it keeps the overall complexity of a tuning way down, even if you wind up with what looks like complex intervals in the tuning, as you can easily verify by ear. It is especially noticeable on an acoustic instrument.
Written I’m guessing in the early 80′s. A contemporary styled classical piece. I moved 3 notes down an octave to give a bit more interest in a chromatic run and added a “F” at the end – which turned out to be the real tonal center.
This was written with trying to imagine the flute in my head and capturing the notes on paper. Some people are really good at this, I’m not – thus the revisions. Still the piece seems to be passable quality for the style it is in.
That being said I used this piece to compare several tuning systems on a purely melodic basis.
The conventional 12 edo tuning
A tuning system that uses the 12th root of phi
12th root pf phi in 12 steps (or perhaps actually 11 steps – I’m still figuring things out)
11
!
69.42116
138.84232
208.26348
277.68464
347.10580
416.52696
485.94813
555.36929
624.79045
694.21161
763.63277
A tuning system posted by Petr of the Tuning List the adjusts 12 equal to the Golden Spectrum
The golden spectrum
12
!
99.27089
198.54178
267.63881
366.90970
466.18059
565.45148
634.54852
733.81941
833.09030
932.36119
1100.72911
1200.000
This is one of my favorite music theory assignment compositions. The voice part didn’t work out too well so it is not presented here.
The goal of the assignment was to use 7th, 9th, 11th, and 13th chords in a somewhat impressionistic manner.
The above video uses Pianoteq in Lucy tuning . When posted to a music site a number of people commented that they thought the Lucy tuned piano sounded out of tune. So I posted the 12 tet version of the performance and the opinions were divided as to what was better. In response I posted a mash up with the left ear 12 tet and the right ear Lucy tuned.
I present this mash up here so you may decide for yourself.
Caleb Morgan on the tuning list posted a piano piece using his 36 note tuning of fractions created in homage to Harry Partch.
I asked and received permission to try his tuning as well as the scala formated tuning itself.
The piece in the video is a sight unseen improvisation using a M-Audio 88es midi controller to drive Pianoteq 3 standalone. I midi recorded the performance via pianoteq and rendered the midi without correction post performance and combined it with video I took of the performance with added effects.
Being an improvisation and a totally new tuning scheme there are “bad” notes and also the exploration section is intact. I can’t say I really grok this tuning though I want to try it again – at an octave or two lower.
Orchestral piece in 22 edo – minimalistic and seems best on headphones
http://clones.soonlabel.com/mp3/daily20100210-22edo-b.mp3
I have been playing with this for about 2 weeks and seem to have come to an impasse. This is a very quirky strange piece – it sounds childish and immature in a way. Reminds me in a very abstract way of the sounds of my neighborhood recorded on my dad’s monaural tape recorder recorded and played back at full amplification.
Garritan Personal Orchestra in 22 edo
brass, woodwind, strings, percussion, choir
The technique to compose this piece is to improvise an instrument’s part and then go back as edit as necessary to remove mistakes or correct intonation.
Not done yet – but I can’t move past at this point.
Part of a planned series examining my childhood aural memories.
Watching it Snow is an edited piano improvisation using M-Audio keystation 88es, Pianoteq, Sonar 8.5, and the Hanson 19 scala tuning file (click the “more” below). That the piece is in Just Intonation is actually an accident! Going by the advice I received from Petr Parízek ( tuning list Message #86387 ) to improvise in Hanson I found Hanson_19.scl and proceeded along with no research whatsoever 
which is how one obtains an inadvertent composition.
This is piece is more melodic than my usual microtonal piece – though I may revise the melody in the beginning sometime in the future to give it more variety.
The score for the piece in pre-translated 12 EDO is here
All of the information for the piece is in this folder
! hanson_19.scl
!
JI version of Hanson’s 19 out of 53-tET scale
19
!
25/24
27/25
9/8
125/108
6/5
5/4
125/96
4/3
25/18
36/25
3/2
25/16
8/5
5/3
125/72
9/5
15/8
48/25
2/1
And here are the intervals those ratios turn out to be. Note – in 12 EDO (“normal” tuning) each half step is 100 cents – so any deviation from 100 cents and multiples thereof (200, 300, ….) is “microtonal” even if the name is the same.
Interval class, Number of incidences, Size:
1: 11 25/24 70.672 cents classic chromatic semitone
2: 7 27/25 133.238 cents large limma
3: 7 9/8 203.910 cents major whole tone
4: 7 125/108 253.076 cents semi-augmented whole tone
5: 15 6/5 315.641 cents minor third
6: 12 5/4 386.314 cents major third
7: 6 125/96 456.986 cents classic augmented third
8: 13 4/3 498.045 cents perfect fourth
9: 11 25/18 568.717 cents classic augmented fourth
10: 11 36/25 631.283 cents classic diminished fifth
11: 13 3/2 701.955 cents perfect fifth
12: 7 25/16 772.627 cents classic augmented fifth
13: 12 8/5 813.686 cents minor sixth
14: 15 5/3 884.359 cents major sixth
15: 9 125/72 955.031 cents classic augmented sixth
16: 10 9/5 1017.596 cents just minor seventh
17: 7 15/8 1088.269 cents classic major seventh
18: 11 48/25 1129.328 cents classic diminished octave
This is a hybrid performance / scored piece using Kontakt 3, pianoteq, sonar 8.5, and a Korg MS2000 as a midi controller.
Kontakt contributes drums, upright bass, sax section, and trumpet.
Pianoteq 2.3 contributes the jazz piano.
The drums were scored first, bass second and then other instruments played along with that. The goal was to keep the composition to 60 seconds or less since this is a submission to the Chicago 60×60 event (not selected at this time).
The main motive is a 17 ET analog to a suspended 4th to major 3rd in common practice 12 edo tuning.