The harmonic bars are are where you can setup the basic “fingerprint” of a sound in Sine Machine.
Each bar represents a harmonic. The height is the volume of the harmonic.
For example, to specify the volume of the fundamental, change the blue bar on the far left.
You can change any harmonic in the harmonic series up to the 36th harmonic. This “basic shape” is the foundation of every note you play.
The max volume of any given harmonic is 1/f, where f is the harmonic number.
Volumes are scaled 1/f
As described earlier, humans enjoy tonal sounds that have most energy at lower harmonics.
Sine Machine automatically scales the maximum amplitude for any given harmonic to 1/f — where f is the number of the harmonic.
This means the 2nd harmonic’s maximum volume 1/2 of the fundamental’s max volume, the third harmonic is 1/3 etc.
With all bars at their maximum value, you get a sawtooth wave.
Note that other additive synths may not do this scaling. We do it because otherwise the higher harmonics become tiny on things like sawtooth/triangles — we want better UX, to have those be easily editable. But also, it better represents how we actually hear things!
Want to create harsher sounds that emphasize higher harmonics? Simply turn down the lower harmonics.
Volumes are volume compensated
With every change to the harmonic volumes, some overall gain compensation is applied to keep the RMS of the waveform similar to a sawtooth. This is to provide a consistent experience and make sure you can move between detailed setups without losing a bunch of gain.
What about harmonics 36 through 512?
An individual note you play could have 10 harmonics or 100 harmonics or 500 harmonics — it depends on how close it is to nyquist.
So on a note with 100 harmonics, what happens with harmonics 37 through 100?
Their volumes are currently set through a rudimentary algorithm:
- Harmonics 30, 32, 34 and 36 will determine a “curve” for the even harmonics above them.
- Harmonics 29, 31, 33, 35 determine a “curve” for the odd harmonics above them.
- The upper harmonics adhere to the volume scale
1/f.
For most cases, harmonics above 36 don’t individually matter. For a sawtooth, the 37th harmonic has 37 times less gain than the fundamental. Pyschoacoustically, this is only about 8x quieter than the fundamental. Higher harmonics do contribute a ton to the overall timbre, especially in bulk with their odd/even neighbors. We used to let all 512 harmonics be individually be edited in the Advanced Mode and expose automation for them, but it was tedious and DAWs (Ableton Live in particular) would choke. I’ve filed a bug report, so maybe someday they’ll make a comeback in the Advanced Mode and ultra-nerds can rejoice.
Volumes are automatable
These individual harmonic volumes are exposed for DAW automation/modulation if you want to get detailed with it!
What about my wavetables?
In a wavetable synth, the core DNA of the sound is scrubbing through different wave shapes. Most of a sound’s complexity is built there, in the DNA of the wavetables.
In Sine Machine, all the complexity happens after the volumes. Think of Volumes as more of a “filter” for all the madness that happens down the line. You are setting the maximum volumes for what each harmonic can output.
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