An implementation of Walter Hewlett's base40 musical pitch and interval numbering system.
These can be initialized in one of two ways:
From a pitch name, where pitch names are written with an uppercase note letter, up to two accidentals of the same type, and an octave number.
>>> Base40Pitch('Cb4')
Base40Pitch("Cb4", 162)
Or from a base40 number value.
>>> Base40Pitch(162)
Base40Pitch("Cb4", 162)
You can get MIDI values from it:
>>> Base40Pitch('A4').midi
69
You can get a lilypond (absolute octave reference) string from it:
>>> Base40Pitch('Cb2').lilypond
'ces,'
You can get the interval distance between two of them:
>>> Base40Pitch('C4').interval(Base40Pitch('Eb4'))
Base40Interval("+m3", 11)
It's worth trying that again with an enharmonic equivalent:
>>> Base40Pitch('C4').interval(Base40Pitch('D#4'))
Base40Interval("+A2", 7)
Magic. Because:
>>> Base40Pitch('D#4') == Base40Pitch('Eb4')
False
Rather:
>>> Base40Pitch('D#4') < Base40Pitch('Eb4')
True
You can invert a note around another note:
>>> Base40Pitch('C4').inverted(Base40Pitch('C5'))
Base40Pitch("C6", 243)
If you add an interval to one, you get what you'd expect:
>>> Base40Pitch('C4') + Base40Interval('P5')
Base40Pitch("G4", 186)
If you subtract an interval from one, you get what you'd expect:
>>> Base40Pitch('Eb4') - Base40Interval('m3')
Base40Pitch("C4", 163)
These can be initialized in one of two similar ways:
From an interval name, with interval names written beginning with a + (for an ascending interval) or a - (for a descending interval), followed by an case-sensitive quality letter, and a quality integer.
The qualities are as follows:
| quality | letter |
|---|---|
| Diminished | d |
| Minor | m |
| Perfect | P |
| Major | M |
| Augmented | A |
>>> Base40Interval('+m3')
Base40Interval("+m3", 11)
Or from a base40 number value.
>>> Base40Interval(-11)
Base40Interval("-m3", -11)
They can be inverted:
>>> Base40Interval(23).inverted
Base40Interval("-P4", -17)
And they can be split into octave and simple form compounds (Note: that the simple value is a base40 number):
>>> Base40Interval('+M9').compound
CompoundInterval(octave=1, simple=6)
They are well behaved when you add them:
>>> Base40Interval('+m3') + Base40Interval('+M3')
Base40Interval("+P5", 23)
and subtract them from one another:
>>> Base40Interval('+P8') - Base40Interval('+P4')
Base40Interval("+P5", 23)
Walter B. Hewlett - A Base-40 Number-line Representation of Musical Pitch Notation.