> Any of the old hands in this group have any commentary why triangle waves 
> have been ubiquitous since the 70s but I've never seen a parabolic?  Indeed, 
> what hardware or software has even offered a parabolic?

For a ramp, you charge a capacitor via a constant current source, discharge the 
cap when it reached a threshold. A triangle is a variation on that (depends 
whether it’s derived or the base waveform for details, but my main point is 
linear segments are easy to make). A square/pulse can be made from that and a 
comparator—again, simple circuitry. Those waveforms not only work well for the 
task, but are handy shapes for testing and other purposes, so had already been 
around a long time in lab signal generators—what the first synthesists had 
available to work with. They fulfill important modulation needs well too.

Very few components to get to that point, most of the oscillator circuitry 
remaining is for tuning and stability over range and temperature. Parabolic 
would be tough for not much gain in a subtractive synth.

> On Feb 10, 2018, at 4:00 AM, Frank Sheeran <fshee...@gmail.com> wrote:
> 
> In my software modular-style synthesizer Moselle (http://moselle-synth.com 
> <http://moselle-synth.com/>) I've added a parabolic waveform.
> 
> As most readers of this list know, it sounds like a "mellow sawtooth" in the 
> exact way a triangle sounds like a mellow square wave. Each harmonic's power 
> is divided by the harmonic number, and every other harmonic's phase is 
> reversed.
> 
> Moselle has several oscillators, but I implemented it in the SWO--Stored 
> Waveform Oscillator, which is by default bandwidth-limited;
> resampled every three semitones up the keyboard; interpolated and 2x 
> over-sampled (8x in the treble).
> 
> Any of the old hands in this group have any commentary why triangle waves 
> have been ubiquitous since the 70s but I've never seen a parabolic?  Indeed, 
> what hardware or software has even offered a parabolic?
> 
> Moselle's SWO implements a PW/PWM waveform by adding an inverted and 
> out-of-phase bandwidth-limited (BWL) sawtooth to another, producing a BWL 
> pulse.  Likewise, it offers a smooth morph between sawtooth and triangle by 
> doing the same trick with parabolics and a little scaling.  (I haven't seen 
> this in the literature but to scale the result to[-1,1] you divide by ( 6 * ( 
> duty - duty * duty ) ).  )  The result isn't simply a sawtooth fading out as 
> a triangle fades in, but rather the maximum point sliding from 0 degrees to 
> 90 degrees (and minimum from 360 degrees to 270 degrees).  Again same 
> question: what hardware or software has offered this waveform?  And it sounds 
> nice so why isn't it more popular?
> 
> <image.png>
> 
> On Fri, Feb 9, 2018 at 2:01 AM, <music-dsp-requ...@music.columbia.edu 
> <mailto:music-dsp-requ...@music.columbia.edu>> wrote:
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> Today's Topics:
> 
>    1. Re: Formants (Robert Marsanyi)
>    2. [JOBS] C++ Developer at Le Sound By AudioGaming
>       (AudioGaming - Jobs)
> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Wed, 7 Feb 2018 10:08:45 -0800
> From: Robert Marsanyi <r...@whidbey.com <mailto:r...@whidbey.com>>
> To: music-dsp@music.columbia.edu <mailto:music-dsp@music.columbia.edu>
> Subject: Re: [music-dsp] Formants
> Message-ID: <cc86381b-5beb-a43c-fb51-b0c6fa0e6...@whidbey.com 
> <mailto:cc86381b-5beb-a43c-fb51-b0c6fa0e6...@whidbey.com>>
> Content-Type: text/plain; charset="utf-8"
> 
> On Tue, Feb 6, 2018 at 8:56 PM, Frank Sheeran <fshee...@gmail.com 
> <mailto:fshee...@gmail.com>
> <mailto:fshee...@gmail.com <mailto:fshee...@gmail.com>>> wrote:
> >
> >     I'm hoping to make some formant synthesis patches with my modular
> >     soft synth Moselle. http://moselle-synth.com <http://moselle-synth.com/>
> >
> >     I've looked around for formant tables and find tables with more
> >     vowels and fewer formants, or fewer vowels and more formants.?
> >     Tables with amplitude seem to have fewer vowels and only one I've
> >     found shows Q.
> >
> I'm interested in the synthesis of consonants.? How are these typically
> handled in a formant-based system?
> 
> --rbt
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> ------------------------------
> 
> Message: 2
> Date: Thu, 08 Feb 2018 14:23:01 +0100
> From: AudioGaming - Jobs <j...@audiogaming.net <mailto:j...@audiogaming.net>>
> To: music-dsp@music.columbia.edu <mailto:music-dsp@music.columbia.edu>
> Subject: [music-dsp] [JOBS] C++ Developer at Le Sound By AudioGaming
> Message-ID: <b7f9368921dc1da37b80378aba15b...@audiogaming.net 
> <mailto:b7f9368921dc1da37b80378aba15b...@audiogaming.net>>
> Content-Type: text/plain; charset=US-ASCII; format=flowed
> 
> Hi,
> 
> Le Sound By AudioGaming (http://lesound.io/ <http://lesound.io/>) is looking 
> for a software
> engineer with experience and passion in audio to help improving our
> audio plugin development framework and implementing customised
> applications.
> 
> Please find more information about the position here:
> 
> https://lesound.io/career_software-engineer/ 
> <https://lesound.io/career_software-engineer/>
> 
> Please send your application or questions to: jobs at audiogaming dot
> net
> 
> Le Sound By AudioGaming
> 
> 
> ------------------------------
> 
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> End of music-dsp Digest, Vol 32, Issue 14
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