Package: pitchclock
PitchClock LogoPitchClockPitchClock is a Python library for generatingtone
clockvisualizations. Tone
clocks were originally developed as a tool for atonal composition, but
can also be quite useful for visualizing tonal structures in classical
andJust Intonationtheory as well.LicensePitchClock is distributed under the permissiveMIT
license.Links:Distribution:https://pypi.python.org/pypi/pitchclockSource:https://github.com/hosford42/pitchclockInstallationThe latest stable distribution of PitchClock can be installed with pip:pip install pitchclockOr, if you prefer the current development version:pip install git+https://github.com/hosford42/pitchclock.gitExample UsageAs an example, let’s compare the equal temperament major scale, versus
the just intonation scale it approximates, known as thesyntonic
diatonic
scale. Tone
clocks are used for visualizing therelationships, i.e. the intervals,
between the pitches, rather than the absolute pitches themselves. Thus
the typical approach is to label the pitches with the intervals from the
tonic that produce them, and to place the tonic at the 12 o’clock
position. The equal temperament intervals are represented as the number
of half-tones in the interval, enclosed within square brackets. The just
intervals are represented as whole number frequency ratios. For this
graph, we will mark the equal temperament intervals with filled circles,
the just intervals with outlined circles, and the tonic with an angle
mark. Here’s the code to produce the graph:fromfractionsimportFractionfrompitchclockimportETInterval,ToneClock# The equal temperament scale, expressed as equal temperament# intervals from the tonic.et_major_scale=[ETInterval(s)forsin[0,2,4,5,7,9,11]]# The just intonation scale, expressed as frequency ratios from# the tonic.ji_major_scale=[Fraction(*pair)forpairin[(1,1),(9,8),(5,4),(4,3),(3,2),(5,3),(15,8)]]# Here we create the clock, indicating which pitches to represent# with each type of marking in the graph.clock=ToneClock(filled_dots=et_major_scale,empty_dots=ji_major_scale,angles=[et_major_scale[0],ji_major_scale[0]],labels={p:pforpinet_major_scale+ji_major_scale})# We make the radius a little bigger because there's a lot going# on in this graph. A bigger radius means more space for details.clock.style.radius*=1.5# Everything is quantized to quarter tones by default, but we are# building this graph specifically to compare slight differences# in pitch, so we turn it off. However, we leave it on for labels,# because otherwise they will overlap for pitches that are very# close neighbors. With quantization of labels left on, labels# falling within the same quantum will be grouped together with# commas to separate them.clock.style.quantize_non_labels=False# Save the clock as a PNG file. Currently, this is the only# supported format.clock.save('images/major_comparison.png')And here’s the image it produces:Major Scale ComparisonFrom this graph, it becomes immediately apparent that the intervals in
the syntonic scale that are most poorly approximated by the equal
temperament major scale are5/4,5/3, and15/8, each of
which is slightly flatter than the equal temperament pitch used to
approximate it.