Carl Lumma

Carl Lumma (b. 1977) is a man with varied interests, including nuclear engineering, macroeconomics, and music theory. Making his home in silicon valley, he has worked as an editor at Keyboard magazine and as a program manager at Apple. Carl has been a moderator of the Tuning and Tuning-math mailing lists. Some of his recent posts are collected here and some ancient posts are here.

Some of his music theory articles:

28-string Cosmolyra after Ivor Darreg

Isomorphic keyboard mapping for 5-limit just intonation

Spectral analysis reveals accurate 7-limit intonation in barbershop music

Archimedean keyboards

Rothenberg stability in pitch space

Stellated Combination Product Sets: How many tones?

Xenharmonic Moving Windows: Extended JI with conventional keyboards

MIDI-based adaptive tuning by common-tone matching

Generalizing diatonicity

Successive improvements in 17-limit TOP damage for the first 100 ETs

Logflat-best rank 1 temperaments up to 100 notes/octave

Classification of microtonal notation systems

No limits: Optimal subgroups for equal temperaments

Measuring the strength of chord progressions

Maximum dyadic error of triads in equal temperaments

The MOS theorem: Well-formed scales are tempered Fokker blocks

Stuff of a more tutorial nature:

Xenharmonic Glossary

The Alternative Tuning FAQ

Cross-sets Primer

The Too-Condensed Tuning-Math Outline

Elsewhere on the web:

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