Carl Lumma
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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 [[http://www.keyboardmag.com|Keyboard magazine]] and as a program manager at [[http://www.apple.com|Apple]]. Below is a partial listing of his music theory articles: [[http://lumma.org/music/theory/cosmo/CosmolyraInstructions.txt|28-string Cosmolyra after Ivor Darreg]] [[http://lumma.org/music/theory/keys/DiatonicCrossSet.png|Isomorphic keyboard mapping for 5-limit just intonation]] [[http://lumma.org/music/theory/spectro/|Spectral analysis reveals accurate 7-limit intonation in barbershop music]] [[http://lumma.org/music/theory/keys/arch/|Archimedean keyboards]] [[Lumma Stability|Rothenberg stability in pitch space]] [[http://lumma.org/music/theory/StellatedCPS.txt|Stellated Combination Product Sets: How many tones?]] [[http://lumma.org/music/theory/XMW.txt|Xenharmonic Moving Windows: Extended JI with conventional keyboards]] [[http://lumma.org/music/theory/AdaptiveTuning.txt|MIDI-based adaptive tuning by common-tone matching]] [[http://lumma.org/music/theory/gd/|Generalizing diatonicity]] [[http://lumma.org/music/theory/TOPDamageOfETs.txt|Successive improvements in 17-limit TOP damage for the first 100 ETs]] [[http://lumma.org/music/theory/TOPBadnessOfETs.txt|Logflat-best rank 1 temperaments up to 100 notes/octave]] [[http://lumma.org/music/theory/notation/|Classification of microtonal notation systems]] [[http://lumma.org/music/theory/subgroup/|No limits: Optimal subgroups for equal temperaments]] [[http://lumma.org/music/theory/ProgressionStrength.txt|Measuring the strength of chord progressions]] [[http://lumma.org/music/theory/MaxETError.txt|Maximum dyadic error of triads in equal temperaments]] The MOS theorem: Well-formed scales are tempered Fokker blocks Stuff of a more tutorial nature: [[glossary|Xenharmonic theory glossary]] [[http://lumma.org/tuning/faq/|The alternative tuning FAQ (draft)]] [[http://lumma.org/music/theory/CrossSetsPrimer.txt|Cross-sets Primer]] [[http://lumma.org/music/theory/tctmo/|The Too-Condensed Tuning-Math Outline]] Carl has been a moderator of the [[http://groups.yahoo.com/group/tuning/|Tuning]] and [[http://groups.yahoo.com/group/tuning-math/|Tuning-math]] mailing lists. Some of his recent posts are collected [[Mailing list articles by Carl Lumma|here]] and some ancient posts are [[http://lumma.org/words/forums/Tuning-CKL97-00.html|here]]. Elsewhere on the web: [[http://www.facebook.com/clumma|Facebook]] [[https://www.youtube.com/user/clumma/|YouTube]] [[http://google.com/+CarlLumma|Google Plus]] [[http://en.wikipedia.org/wiki/Special:Contributions/Beefman|Wikipedia contributions]]
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<html><head><title>Carl Lumma</title></head><body><strong>Carl Lumma</strong> (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 <a class="wiki_link_ext" href="http://www.keyboardmag.com" rel="nofollow">Keyboard magazine</a> and as a program manager at <a class="wiki_link_ext" href="http://www.apple.com" rel="nofollow">Apple</a>. Below is a partial listing of his music theory articles:<br /> <br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/cosmo/CosmolyraInstructions.txt" rel="nofollow">28-string Cosmolyra after Ivor Darreg</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/keys/DiatonicCrossSet.png" rel="nofollow">Isomorphic keyboard mapping for 5-limit just intonation</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/spectro/" rel="nofollow">Spectral analysis reveals accurate 7-limit intonation in barbershop music</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/keys/arch/" rel="nofollow">Archimedean keyboards</a><br /> <a class="wiki_link" href="/Lumma%20Stability">Rothenberg stability in pitch space</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/StellatedCPS.txt" rel="nofollow">Stellated Combination Product Sets: How many tones?</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/XMW.txt" rel="nofollow">Xenharmonic Moving Windows: Extended JI with conventional keyboards</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/AdaptiveTuning.txt" rel="nofollow">MIDI-based adaptive tuning by common-tone matching</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/gd/" rel="nofollow">Generalizing diatonicity</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/TOPDamageOfETs.txt" rel="nofollow">Successive improvements in 17-limit TOP damage for the first 100 ETs</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/TOPBadnessOfETs.txt" rel="nofollow">Logflat-best rank 1 temperaments up to 100 notes/octave</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/notation/" rel="nofollow">Classification of microtonal notation systems</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/subgroup/" rel="nofollow">No limits: Optimal subgroups for equal temperaments</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/ProgressionStrength.txt" rel="nofollow">Measuring the strength of chord progressions</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/MaxETError.txt" rel="nofollow">Maximum dyadic error of triads in equal temperaments</a><br /> The MOS theorem: Well-formed scales are tempered Fokker blocks<br /> <br /> Stuff of a more tutorial nature:<br /> <a class="wiki_link" href="/glossary">Xenharmonic theory glossary</a><br /> <a class="wiki_link_ext" href="http://lumma.org/tuning/faq/" rel="nofollow">The alternative tuning FAQ (draft)</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/CrossSetsPrimer.txt" rel="nofollow">Cross-sets Primer</a><br /> <a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/" rel="nofollow">The Too-Condensed Tuning-Math Outline</a><br /> <br /> Carl has been a moderator of the <a class="wiki_link_ext" href="http://groups.yahoo.com/group/tuning/" rel="nofollow">Tuning</a> and <a class="wiki_link_ext" href="http://groups.yahoo.com/group/tuning-math/" rel="nofollow">Tuning-math</a> mailing lists. Some of his recent posts are collected <a class="wiki_link" href="/Mailing%20list%20articles%20by%20Carl%20Lumma">here</a> and some ancient posts are <a class="wiki_link_ext" href="http://lumma.org/words/forums/Tuning-CKL97-00.html" rel="nofollow">here</a>.<br /> <br /> Elsewhere on the web:<br /> <a class="wiki_link_ext" href="http://www.facebook.com/clumma" rel="nofollow">Facebook</a><br /> <a class="wiki_link_ext" href="https://www.youtube.com/user/clumma/" rel="nofollow">YouTube</a><br /> <a class="wiki_link_ext" href="http://google.com/+CarlLumma" rel="nofollow">Google Plus</a><br /> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Special:Contributions/Beefman" rel="nofollow">Wikipedia contributions</a></body></html>