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TES: The largest network of teachers in the world

Portions not contributed by visitors are Copyright 2018 Tangient LLC

TES: The largest network of teachers in the world

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Carl Lumma(b. 1977) is a man with varied interests, including nuclear engineering, macroeconomics, music theory, and artificial intelligence. Making his home in the San Francisco area, he has worked as an editor at Keyboard magazine and as a program manager at Apple. Below is a partial listing 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 (draft)

Cross-sets Primer

The Too-Condensed Tuning-Math Outline

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.

Elsewhere on the web:

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Wikipedia contributions