Trumpet, Horn, Trombone (duh!), Tuba, digeridoo, alphorn
bwhisperer.com JI-oriented website, "The Brass Whisperer's main aim is to play with subtle music tunings and coax brass players (and other musicians) into achieving delicious harmonies."
Trumpet, Horn, Trombone (duh!), Tuba, digeridoo, alphorn
bwhisperer.com JI-oriented website, "The Brass Whisperer's main aim is to play with subtle music tunings and coax brass players (and other musicians) into achieving delicious harmonies."
No-13's "Harmonic" Mode - does it belong here?
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No-13's "Harmonic" Mode - does it belong here? While playing around with combination product sets, I happened upon a neat heptatonic mode that tou…
No-13's "Harmonic" Mode - does it belong here? While playing around with combination product sets, I happened upon a neat heptatonic mode that touches on all the harmonics well-represented in 22edo. It is comprised of degrees 0-2-7-10-13-18-20-22, or step sizes [2 5 3 3 5 2 2]. In this "home" position, it represents a tempering of (1/1, 17/16, 5/4, 11/8, 3/2, 7/4, 15/8, 2/1). Other rotations of the tempered yield interesting results too.
However, this page seems to be all MOS all the time, so I'm wondering whether it's appropriate to put it here.
Synch-Meantone
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Synch-Meantone 69edo's fifth is extremely close to that of "Synch-Meantone" in Scala, or Wilson equal be…
Synch-Meantone 69edo's fifth is extremely close to that of "Synch-Meantone" in Scala, or Wilson equal beating meantone. Thought that was interesting.
Perhaps someone could help figure out how perceptually "off" 69edo is from the real thing? Like, how long does it take for the beat-rates of the fifth and thirds to noticeably go out of sync..
POTE tuning
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... tuning enforcing a just 2s as octaves. 2/1 octave.
The POTE tuning for a map matrix suc…
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tuning enforcing a just 2s as octaves.2/1 octave.
The POTE tuning for a map matrix such as M = [<1 0 2 -1|, <0 5 1 12|] (the map for 7-limit magic, which consists of a linearly independent list of vals defining magic) can be found as follows:
#1 Form a matrix V from M by multiplying by the diagonal matrix which is zero off the diagonal and 1/log2(p) on the diagonal; in other words the diagonal is [1 1/log2(3) 1/log2(5) 1/log2(7)]. Another way to say this is that each val is "weighted" by dividing through by the logarithms, so that V = [<1 0 2/log2(5) -1/log2(7)| <5/log2(3) 1/log2(5) 12/log2(7)]
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#3 Find T = <1 1 1 1|P.
#4 Find POTE = T/T[1]; in other words T scalar divided by T[1], the first element of T.
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should find
V ~ [<1 0 0.861 -0.356|, <0 3.155 0.431 4.274|]
T ~ <1.000902 0.317246|
Porcupine
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... The specific tuning shown is the full 11-limit POTE tuning, but of course there is a range of …
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The specific tuning shown is the full 11-limit POTE tuning, but of course there is a range of acceptible porcupine tunings that includes generators as small as 160 cents (15edo) and as large as 165.5 cents (29edo). (However, the 29edo patent val does not support 11-limit porcupine proper, not annihilating 64/63.)
12/11, 11/10, and 10/9 are all represented by the same interval, the generator. This makes chords such as 8:9:10:11:12 exceptionally common and easy to find.
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in just intonationintonation.
All intervals are slightly different.
Porcupine-tempered 8:9:10:11:12 chord, in 22edo22edo.
Except the first, the intervals <re the same.
Porcupine-tempered 8:9:10:11:12 chord, in 29edo29edo.
Except the first, the intervals are the same.
The 11/9 interval, usually considered a "neutral third", is in porcupine identical to the 6/5 "minor third". This means that the 27/20 "acute fourth" of the JI diatonic scale is equivalent to 11/8 (rather than becoming 4/3 as in meantone).
The characteristic small interval of porcupine, which is 60.75 cents in this tuning but can range from <50 to 80 cents in general, represents both 25/24 and 81/80.