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Short listening example
It's hard to imagine the effect, I tried to build something with Csound, but didn't have much luck. Do you have an audio (link/download) example at hand? Thanks :-)
- xenwolf February 22, 2016, 12:26:23 PM UTC-0800
Here's a YouTube upload. I was able to get a successful result with 10edo. The synthtone I ended up with sounds a bit like an electric organ.
The timbre in question was built from the first 8 partials. The total amplitude of each partial is proportional to 1/(N^1.5) where N is the number of the partial.
The 3rd, 5th, 6th, and 7th partials all have two components, about equal in amplitude separated by about 50-60 cents. Although I stopped at 8, it could easily be extended beyond the 8th partial (in particular, the 13th partial is so close in 10edo that it wouldn't even be necessary to introduce an inharmonic component).
One notable effect of doing this is that it changes not only how harmonies are perceived, but also melodies as well. The 10edo synth tone sounded better to my ear with 10edo mohajira than with the 12edo diatonic scale. In addition, it also messes with absolute pitch sensing (I normally have perfect pitch, but with this mixed timbre, the "C" doesn't sound as much like a C anymore, although it still has a well-defined pitch. The relationship of fundamental frequency to the pitch "color" or chroma becomes different).
My next project will be to do something with a non-octave scale (probably BP or 26edt). I will need to figure out a way to "disable" the listener from perceiving octaves, so as to enable the tritave to come into its own as an interval of equivalency. That may prove to be difficult, although it's worth a try. Probably introducing a highly mistuned octave (or diffuse white noise around where the 2nd harmonic "should" be) will do the trick. I'll let you know as soon as I have a result.
- MasonGreen1 March 04, 2016, 07:06:53 PM UTC-0800
And here's one for 17edo:
- MasonGreen1 March 04, 2016, 10:38:35 PM UTC-0800
Okay, I'm getting the idea. Thanks for sharing your work (you know that YouTube videos -- and much more -- can also be embedded in the wiki?). It reminds me of William Sethares and his research about tuning and timbre. BTW: I hear some artefacts in the recordings. How did you create the sound?
- xenwolf March 05, 2016, 08:38:26 AM UTC-0800
I used Audacity. Basically just added sine waves together. Then (to make the melody/chord demonstrations), I imported the .WAV files into LMMS. And then I uploaded the whole thing via Windows Movie Maker to YouTube. There definitely was a loss of sound quality during the process; it sounded much better in the original Audacity.
I've been doing some more experiments and I've found something very interesting by comparing the following sounds:
A. Ordinary square wave
B. Square wave with 7th partial removed
C. Square wave with 7th partial replaced with mistuned version
D. Square wave with BOTH harmonic and inharmonic versions of 7th partial.
A and B both sounded good (well, as good as a square wave can; they're pretty harsh by nature). But D sounded much, much better than C. C sounded very unstable to me. It does appear that at least in this situation, it's better to have both, than to just have the inharmonic one by itself.
It also appears as though the ear is more tolerant of inharmonicity involving higher partials than lower ones. So it'd be hard if not impossible to make a timbre that "sounds harmonic" yet also works with something like 13edo, for instance.
I've read about Sethares' work before, although I'm not too familiar with it; it's possible I might be independently rediscovering some of his ideas.
I'm still learning how to use the wiki, hopefully soon I'll get around to figuring out how to embed more stuff.
- MasonGreen1 March 14, 2016, 01:29:26 AM UTC-0700
Thanks for the explanation. As for the quality loss: Did you try Csound (or Supercollider) before? I think Csound could be quite good for your task.
- xenwolf March 14, 2016, 03:33:06 AM UTC-0700
I'm not familiar with Csound yet. I'll look it up, it sounds interesting, thanks for the suggestion!
By the way, one of the people I played my 10edo / 17edo sounds for said he thought they sounded "too high" and would sound better if lower-pitched. I think he might have been on to something. Especially when dealing with higher-limit harmonies (in which the 11th or higher partials play a major role), it seems like using a lower tessitura or register is a good idea. If the fundamental is 1000 Hz then the eleventh harmonic will be 11 kHz, which is uncomfortably high.
Simple waveforms like sine or square waves sound indistinct at very low pitches. However, the story changes for more complex waveforms. A "no-fives" sawtooth wave with all multiples-of-5 harmonics removed sounds much clearer at low pitches and can be used farther into the bass range. Removing the multiples of 17 and 19 makes the sound even clearer still and results in a very jagged, "fractal-looking" wave. (Removing 5, 17, and 19 works very well with 17edo since it doesn't match those harmonics as well as the others).
Another option I haven't explored yet is to add _fractional_ partials (such as 13/5 times the fundamental frequency, etc). I'm not sure if there's a name for such a partial; a fractional partial could be considered to be a harmonic of a subharmonic, or a subharmonic of a harmonic. Maybe fractional partials could be called "paraharmonics"? They, like harmonics and subharmonics, can display mode-locking (although the effect is not quite as strong). The amplitude of a paraharmonic can't be _too_ high or else it will muddy the clearness of the note, but they nonetheless seem to be a promising option and they offer a wealth of new possibilities.
Timbres with paraharmonics might be a good fit for 29edo, since it has several harmonics that are very flat but by roughly the same amount, so the ratios between them are much better. (E. g., 7/5, or 13/11).
- MasonGreen1 March 22, 2016, 08:10:44 PM UTC-0700