Another old recording from a couple of years back. Stripped back, voice and piano. Keen to redo this one in a bit

What I Used To Be

I've been fiddling around with 31 tone Equal Temperament recently, but have only just delved into extended keyboard mappings. 

This one is 19 tones to the octave (C C# Db D D# Eb E E# F F# Gb G G# Ab A A# Bb B B#), so it's a bit tough getting used to one octave being 19 semitones on a keyboard. As you can hear still working out where my fingers are going, but it's a start. 31TET is pretty great for anything 7-limit or below (and much prettier than 19TET imo), but the 11 and 13 identities suffer a bit.

More to come.

19 of 31TET Septimal Improvisation

Bosanquet Axis: Exploring 2,3,7,11,13 In 46edo 2014/01/12

Finally came up with an ok 13-limit Just Intonation mapping for the Axis keyboard (also planning to use with the Terpstra), 41 tones to the octave.

Still trying to learn chord shapes as 5/4 major thirds are reached by diminished fourths, harmonic sevenths are double diminished octaves, and 11/8 neutral fourths are triple diminished sixths or triple augmented seconds. Perhaps not the easiest layout to play quick harmony in but a crazy amount of perfect intervals, a crazy amount of very close 'virtually tempered' intervals, and then some interesting oddballs too.

According to scala the scale contains 428 unique intervals... So certainly a lot more different flavours than 41edo!

I've already posted the axis mapping file on XA2 but for anyone interested in JI ratio sets here is the scale:

 0:          1/1               0.000000 unison, perfect prime
  1:         64/63             27.264092 septimal comma, Archytas' comma
  2:         33/32             53.272943 undecimal comma, al-Farabi's 1/4-tone
  3:         22/21             80.537035 undecimal minor semitone
  4:         16/15            111.731285 minor diatonic semitone
  5:         12/11            150.637059 3/4-tone, undecimal neutral second
  6:         10/9             182.403712 minor whole tone
  7:          9/8             203.910002 major whole tone
  8:          8/7             231.174094 septimal whole tone
  9:          7/6             266.870906 septimal minor third
 10:         13/11            289.209719 tridecimal minor third
 11:          6/5             315.641287 minor third
 12:         11/9             347.407941 undecimal neutral third
 13:          5/4             386.313714 major third
 14:         14/11            417.507964 undecimal diminished fourth or major third
 15:          9/7             435.084095 septimal major third, BP third
 16:         21/16            470.780907 narrow fourth
 17:          4/3             498.044999 perfect fourth
 18:         27/20            519.551289 acute fourth
 19:         11/8             551.317942 undecimal semi-augmented fourth
 20:          7/5             582.512193 septimal or Huygens' tritone, BP fourth
 21:         10/7             617.487807 Euler's tritone
 22:         16/11            648.682058 undecimal semi-diminished fifth
 23:         40/27            680.448711 grave fifth
 24:          3/2             701.955001 perfect fifth
 25:         32/21            729.219093 wide fifth
 26:         14/9             764.915905 septimal minor sixth
 27:         11/7             782.492036 undecimal augmented fifth
 28:          8/5             813.686286 minor sixth
 29:         13/8             840.527662 tridecimal neutral sixth
 30:          5/3             884.358713 major sixth, BP sixth
 31:         22/13            910.790281 tridecimal major sixth
 32:         12/7             933.129094 septimal major sixth
 33:          7/4             968.825906 harmonic seventh
 34:         16/9             996.089998 Pythagorean minor seventh
 35:          9/5            1017.596288 just minor seventh, BP seventh
 36:         11/6            1049.362941 21/4-tone, undecimal neutral seventh
 37:         15/8            1088.268715 classic major seventh
 38:         21/11           1119.462965 undecimal major seventh
 39:         64/33           1146.727057 33rd subharmonic
 40:         63/32           1172.735908 octave - septimal comma
 41:          2/1            1200.000000 octave

41-tone BosanquetAxis JI Harpsichord Exploratory Improv 1

Just as the name suggests, a silly little collection of christmasy songs made just after christmas. I figured I might as well share it with you. Certainly not a masterpiece.

All one-take improvisations, recorded off the demo version of Pianoteq (with unplayable notes and all!), tuned in 50EDO (close to 2/7 comma meantone), on a little 2-octave Bosanquet arranged Axis 49.

winter wunderland

silent nite

rudolph

jngle blls

A neat wee 'hyperchormatic' sequence I discovered when getting back into 31EDO a few days back. Pretending the tonic is C (not C^), the basic progression goes something like: C - C maj7(15) - C harm21(8:12:14:21)-F maj9/C - C harm11(e.g. 4:6:7:10:11) - Ab aug6/C (5:8:12:14 from C) resolving outward to G generally.

So we have the descending line C-B-A#-A-A#-Ab-G and the ascending line E-E#-F-F^-F#-G. Woohoo for hyperchromatic contrary motion.

Back To 31: Hyperchromatic Progression On C^

A series of enharmonic modulations in 50EDO, starting in Gbb major and modulating into F major, sometimes quite naturally, sometimes the jump is a bit more noticeable. In 50EDO F major is 2 steps lower than Gbb, or exactly a quarter of the regular (mean) tone, and it's definitely a strong interval.

I love this sort of thing to lull the listener into thinking they're returning to the original tonic and then whacking them in the face. At the end we go from E# to F back to Gbb major - a full 4 steps or half of a meantone!!!

Enharmonic Modulations in 50EDO

Using an overdriven rhodes sound to demonstrate how awesome 50EDO is for thirds. Here are most of the thirds, used once each in the sequence. ~15/13 (240c), 7/6 (264c), 13/11 (288c), 6/5 (312c), 17/14 (336c), 5/4 (384c), 9/7 (432c), 13/10 (456c). Which means I've only missed out 16/13 and 81/64(or a mistuned 14/11 if you like).

See if you can work out what's going on by ear. I tried to make the difference tones as obvious as I could by using the gnarliest overdriven sound I could find. I quite like this little chord sequence, but might expand it to try and fit in the other two types of thirds.

Definitely a demo, a few muckups trying to find my way around unfamiliar tonal territory... Enjoy!

Chord sequence for Difference tones in 50EDO

not too much to be said. deconstruction of otonal chords

Fragment In Fifty

Exploring what is pretty much a 17-tone subset of 56EDO, with one pitch shifted half a step up to provide 15 regular 56EDO fifths and 2 meantone fifths from 112EDO.

56EDO is an interesting tuning right in the inverse gentle range, where d3~14:13, A1~12:11, d4~11:9 and A2~16:13, plus we also get a fairly good if slightly wide 11:8 from our regular diminished fifths, and a nearly just 28:27 "Archytan" minor second

Very interesting melodic tuning with some crazy harmonic possibilities.

The upcoming Terpstra keyboard will have 56 keys per octave, so I thought this might be a good intro to the world of slightly wide fifths and middle intervals for Africa.

17_112EDO Circulating 2.3.7.11.13 Floaty Piano Improv

Giving 19edo a proper go. I've found the virtually pure 6:5 minor third, 14:13 minor second and 28:27 augmented unison of its meantone tuning [virtually identical to 1/3-comma] very appealing, although it's a tuning system that needs space to really be understood by the ear, so take a seat on the 19edo sofa and feel yourself slowly sink down.

It's a wonder 19(1/3-comma)'s not been more popular (though it has had a small share of keen exponents since the early 16th century) - full circulation and transposability in only 19 keys, each with inframinor, minor, major and ultramajor harmonies available. Here I've made use of the pure minor thirds and slightly beating major thirds on offer. 3:2, 5:4 and 9:5 are all 1/3-comma flat of just, while their inverses 4:3, 8:5 and 10:9 are all 1/3-comma sharp. Still, 1/3-comma (just over 7c) seems like a pleasant little amount of beating most of the time, still only about half of the impurity of 5:4 and 6:5 in 12edo.

Wurly Minors And Enharmonic Tetrachords (17 out of 19edo)

37edo is weird. the diatonic scales have steps of ~7:8 and ~49:50 (i.e. really big major seconds and really small minor seconds), but primes other than 3 connect in rather interesting ways.
here, 5:6 is tempered together with 64:77=(8:7)x(8:11), and so 5:6 and 8:11 are a regular (large) major second apart. the diatonic diesis (i.e. between Bbb and A) is around 10:11, and also represents 11:12, as well as 9:10. strangeness ensues.

37edo wurly: mutability

Pianoteq improv on the axis in 63edo, exploring pivots between otonal chords involving primes 2.3.7.11.13.23 and very occasionally 5. As usual, lots of use of the 3\ diesis, it's one of the key pieces connecting lots of harmonic areas as it represents 32:33, 27:28, 88:91, 1024:1053, 512:529, 117:121, and two of them makes 14:15=15:16 (224:225 tempered out)

63EDOBosanquetAxis 8thJuly2016: 2.3.7.11.13.23 Seconds and Otonal Shifts

17-out-of-19EDO bright objects

Real simple melody/harmonic outline that's been floating around for a long while. Based on probably the most famous ancient Enharmonic scale given by Ptolemy, with the tetrachord of 1/1 28/27 16/15 4/3, though approximated here in 31 tone equal temperament and filled out with harmonic roots E A and D: E F# Fx G A B B# C D
(for any temperament fiends, 31TET is pretty much 1/4 comma meantone extended to 31 keys... and sorry for the low E string, pretty variable pitch there)

A bit of a return to the older harmonies, never a bad thing

Enharmonic melody for guitar

Demo of a song from earlier this year, was playing round with some close BVs and my 31 tone guitar. Need better recording gear though...

what use is a boy

improviser, songwriter, composer, hexagonal keyboardist, tuning buff, renaissance music lover and occasional barbershopper. i made another channel here with a few longer keyboard improvisations, please check it out if you've got time:
https://soundcloud.com/cam-taylor-2-1

Ran out of space on both of my soundcloud accounts so have also posted pieces to https://archive.org/details/@iamcamtaylor

Cam Taylor

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