Consonance is the sense that notes fit together. Tuning decides which pitches are available in the first place. This page lists eleven sources, oldest first where dated. Two ask how listeners come to accept noise and difficult music.
Harmony Explained
A preprint that tries to derive the major scale and chords from physics and computation. This wiki has read only its abstract and the discussion around it, and says so.
John Coltrane's Tone Circle
A long reading of the drawing known as Coltrane's tone circle. It gathers competing interpretations, from scales to geometry to mysticism. It is included because it shows how much meaning can gather around one diagram.
The cultural evolution of distortion in music (and other norms of mixed appeal)
The paper links musical distortion to nonlinear phenomena in animal vocal signals. It adds an agent-based model of how groups choose a timbre norm. Only the abstract was read, so model details and results are unknown.
Show HN: See chords as flags – Visual harmony of top composers on musescore
The thread opens with the creator describing Rawl, a piano roll coloring each scale degree. Replies debate whether such a view beats sheet music for harmony. The poster answers many questions about the color design and annotation work.
Harmony Explained on Hacker News
A thread of 114 comments on Wilkerson's paper. Musicians dispute whether simple ratios and fixed feelings explain musical experience. The paper's author joins in and asks people to read it first.
Music theory for programmers
A long tutorial that derives notes, scales and chords in runnable JavaScript. Its strength is treating tuning as a compromise you can compute. Its critics say it is mostly acoustics rather than theory.
Music Theory for Programmers on Hacker News
A thread of 249 comments on the Haas tutorial. Trained musicians argue that it is acoustics rather than theory. Others debate how much of music is physics and how much is convention.
Music Theory for the 21st-Century Classroom
The thread discusses an open college textbook hosted by the University of Puget Sound. Replies wander from the book itself to notation, tuning and how theory should be taught. Many commenters are working musicians or programmers who disagree with each other.
xenharmlib documentation
Documentation for a free Python library that calculates with scales in many tunings. It is a toolset, not an argument. It is the practical end of this subject.
A beginner's guide to modern classical music
Luke Muehlhauser lists dozens of recordings in playlists, ordered from most accessible to least. The post tells how the author came to love the genre. It offers a listening quiz and guesses why the music is unpopular. It cites no data.
What’s new in xenharmlib 0.4.0?
The page announces xenharmlib 0.4.0 and walks through its new features with short code samples. The main change is support for Just Intonation and other regular temperaments. Evidence is the library's own example output, written by its developer.
Connections to other subjects
These links are this wiki's own reading, not claims the sources make.
- John Coltrane's Tone Circle and What Heraldry and Japanese Mon Can Teach Us About Building Visual-Identity Generators, from Images made by rules. Overmyer asks which rules belonged to a tradition and which came afterward from its explainers. Hollander collects many readings of one Coltrane drawing. The same question applies: which of this geometry was Coltrane's?
- Harmony Explained on Hacker News and Human Judgment as a Specification, from Checkable specs for coding agents. PICK assumes some truth lives only in the person asked. The harmony thread keeps arriving there too. So PICK's method might suit tuning. Generate candidates, find where they differ, and let ears vote.
- Music theory for programmers and Alternate Clock Designs & Time Systems, from Images made by rules. Both ask why a cycle has the divisions it has. The day's are inherited, de Chardon says. Haas shows the octave's twelve are a compromise. A tuning is a clock for the octave.
- xenharmlib documentation and Alternate Clock Designs & Time Systems, from Images made by rules. De Chardon redivides the day and shows what changes. xenharmlib does the same for the octave, with options such as 31 equal steps. Each lets you ask what a new division makes easier.
- A beginner's guide to modern classical music and Developing Taste, from Review, taste and expertise. Kowalski says taste grows from exposure and from explaining why things work. Muehlhauser's guide turns exposure into a route, from film scores toward harder music. Could anyone write that route for reading code?
- The cultural evolution of distortion in music (and other norms of mixed appeal) and Developing Taste, from Review, taste and expertise. Bryant and Smaldino say distortion norms persist partly because groups must differ from each other. Kowalski tells readers to follow a curated list of tastemakers. Together they raise a sharp question. How much of taste in software is a marker of belonging?
- John Coltrane's Tone Circle and Foucault's Pendulum, from Occult, myth and religion. Eco's editors build a grand Plan from a note that proves a laundry list. Hollander collects many readings of one Coltrane drawing. They show how much meaning a pattern can carry once people want it.
Glossary
- Agent-based model
- A simulation in which many simple virtual individuals follow rules and interact.
- Atonal
- Music that has no central key or home note.
- C clef
- A clef that marks where middle C sits, used by viola and some other instruments.
- Cadence
- A short chord pattern that ends a phrase, such as V to I.
- Cents
- A pitch measure, with 1,200 to the octave.
- DAW
- Software for recording and arranging music, short for digital audio workstation.
- Enharmonic
- Describes two written notes, such as A sharp and B flat, sharing a pitch.
- Equal temperament
- A tuning that divides the octave into equal steps.
- Generator interval
- An interval that is stacked repeatedly to produce all the notes of a tuning.
- Interval class vector
- A count of how often each interval type appears among the notes of a set.
- Just intonation
- A tuning built from simple frequency ratios.
- Meantone
- A family of tunings that flatten the fifth slightly to improve the thirds.
- Minimalism
- A style built on repeating a few short musical phrases with slow change.
- Nonlinear phenomena
- Irregular sound features, such as roughness or chaos, in animal and human voices.
- Norm
- A shared habit or standard within a group.
- Piano roll
- A grid view of music where each note is a bar placed by pitch.
- Pitch class
- A note regardless of its octave.
- Postminimalism
- Minimalism that is mixed with other influences such as romantic harmony.
- Pythagorean comma
- The small gap between twelve pure fifths and seven octaves.
- Pythagorean tuning
- A tuning built by stacking pure fifths, each a 3 to 2 ratio.
- Regular temperament
- A tuning in which every note is built from a few repeated generator intervals.
- Roman numeral analysis
- A way of naming chords by their place in a key, like I or V.
- Scale degree
- A note's numbered position in a scale, counted from the tonic.
- Schenkerian analysis
- A method of reducing a piece to its underlying harmonic and melodic structure.
- Secondary dominant
- A chord that briefly acts as the V of a chord other than the tonic.
- Serialism
- A method of composing that applies a fixed series of notes or other elements.
- Shape notes
- A teaching notation that gives each scale degree a distinct note-head shape.
- Timbre
- The tone quality that distinguishes one sound source from another.
- Tonic
- The home note of a key, the one that feels like a resting place.
- Voice leading
- The way each separate line of a chord progression moves from note to note.
- Whole-tone scale
- A six-note scale with equal steps of two semitones.
- Xenharmonic
- Describes music that uses tunings beyond the standard twelve equal steps per octave.