A fun little piece written in Negri temperament, tuned to 19edo (19 equal divisions of the octave).
The idea behind Negri temperament is that 3 semitones (of 16/15) makes a major third (of 5/4), and 4 make a perfect fourth (of 4/3). I use Negri's 9 note Moment of Symmetry Scale in it's disjuct pentachordal mode Negri[9] 4|4, which in 19edo is steps of 222232222. The three step interval is the disjuct tone (9/8) between the tetrachords and the two step interval is the semitone mentioned above. So in 19edo Meantone notation the scale is C Db D# E F G Ab A# B C.
The interval from a Db to a D# and from an Ab to an A# in 19edo are the same. D# and A# are 'interspetimals' representing 7/6 and 8/7 and 7/4 and 12/7 respectively.
The piece starts with a Negri comma pump filling a bar of 7 4. Repetitions of this comma pump make the A section ( The piece is in Ternary form). The comma that is tempered out is what defines the temperament. So the Negri comma is the difference between three semitones of 16/15 and a major third of 5/4 (or between 4 semitones and a perfect fourth of 4/3), equal to 16875/16384. (The meantone comma, which you may be used to, if not aware of, is 81/80, the difference between the major and minor tones 9/8 and 10/9, hence the name 'meantone' when this difference is tempered out. The major scale is the 7 note Moment of Symmetry Scale of Meantone Temperament) A comma pump is a chord progression that leads to the tonic only if the comma is tempered out. The meantone comma pump is a I-vi-ii-V-I progression in it's simplest form. The Negri comma pump I used involves going up a major third and down a fourth four times to get to V, and then up a fourth back to I. Music is available if anyone is curious or has a 19edo guitar and what's to record it :). I will build the flute to play it eventually...

Negri Shmegri

Excerpt from Besaxung-Album "Go!"
Composition P. Gerschlauer

Besaxung:
Philipp Gerschlauer (Sax)
Felix Roßkopf (microtonal Keyboard)
Reza Askari (Bass)
Thomas Sauerborn (Drums)

www.gerschlauermusic.com
www.besaxung.com

Mr. P (comp. Gerschlauer) with Besaxung

Superpyth temperament can be thought of as a mirror opposite of meantone temperament. In meantone temperament four fifths reduced an octave is equated to the 5-limit just major third 5/4, where 4 pure fifths of 3/2 reduced an octave give 81/64, larger than 5/4 by the meantone comma, 81/80. In quarter comma meantone each fifth is flattened by a quarter of this comma so that four of them reduced an octave give an exact 5/4 and the meantone comma is tempered out. In superpyth four fiths reduced an octave is instead taken to be equivalent to the septimal, supermajor third 9/7. Two fourth then give the harmonic seventh 7/4. In quarter-comma superpyth  each fifth is sharpened by a quarter of the archytas comma 64/63, the difference between two fourth of 4/3 and a harmonic seventh of 7/4 then tempered out and fourth fifths reduced an octave giving a pure 9/7. Quarter-comma meantone can be well approximated in 31edo (equal divisions of the octave), and quarter-comma superpyth in 22edo. Diatonic notes in Meantone are 5-limit (subgroup 2.3.5), where chromatic intervals may be septimal (7-limit), i.e. the augemented sixth is 7/4 and the diminished fourth is 9/7. Diatonic notes in superpyth are of the 2.3.7 subgroup, with major and minor thirds at 9/7 and 7/6 respectively. Chromatic intervals may be 5-limit, ie an augmented second of 5/4 and a diminished fourth of 6/5. Using a gamut of Ab-C# (traversed by fifths - the generator), the black notes host the octave species of the 5-limit enharmonic trichord, the 5-note scale: 1/1:5/4:4/3:3/2:15/8, our regular 5-limit M3, P4, P5 and M7. This study is a 5 chord riff that makes use of the 5-limit chromatic intervals of Superpyth[12] (12 notes of superpyth temperament generated by a continuous string of fifths), along with the diatonic intervals. The chords include the diatonic subminor seventh, subminor major seventh and included supermajor seventh, along with the chromatic major and minor seventh chords.

Superpyth[12] chromatic riff

Strange Waves

AssHat

3/2=695 cents, 2/1=1205 cents

I stole the original image from google images. Sorry original content creator.

Memore (in approximately 19 tone equal temperament)

5-ed2, thanks to Sean Archibald for the title.

Ouch My Causality (in 5 tone equal temperament)

3/2=701, 5/4=387

Made using The Viking, a synth from dynamictonality.com, and a free drum plugin.

The scale repeats at the "fifth" (aka the 3/2), and is generated by the "major third" (5/4). I shrunk the 3/2 and stretched the 5/4 slightly so that there was a bigger contrast between the large and small step in the scale.

The scale structures are Mavila-esque, and the tuning here is pretty close to 11-ed3/2

The Stupistest Freakin' Decision (in approximately Carlos-Alpha Tuning)

Initial improv in the following 10-note 5-limit JI scale:
10/9 9/8 5/4 4/3 40/27 3/2 5/3 27/16 15/8 2/1

This scale contains both the Pythagorean (3-limit) pentatonic scale:
9/8 4/3 3/2 27/16 2/1 on every second step.
And the Ptolemaic sequence, the just diatonic scale:
9/8 5/4 4/3 3/2 5/3 15/8 2/1
As well as another tetrachordal just diatonic scale:
10/9 5/4 4/3 3/2 5/3 15/8 2/1

Both tetrachordal just diatonic scales are trivalent, which means that each generic interval, i.e. 2nd (a ‘step’), 3rd, 4th, etc., comes is three specific sizes.

The entire 10-note scale may be described as LsmsLsLsms, where ‘L’ designates a large step, ‘m’ designates a medium sized step, and ‘s’ designates a small step. It has 5 large steps of 10/9, the minor tone; 2 medium sized steps of 16/15, the diatonic semitone; and 3 small steps of 81/80, the syntonic (Meantone) comma. It is not trivalent however the total number of specific intervals is less than for a trivalent scale of the same cardinality. It has 3 sizes of 2nd and 10th, 2 sizes of 3rd, 5th, 7th and 9th, and 4 sizes of 4th, 6th and 8th. It is also invariant under inversion, which means that it’s inversion:  
16/15 32/27 6/5 4/3 27/20 3/2 8/5 16/9 9/5 2/1, is one of its modes. It is an example of a class of scale I have recently discovered, which I am calling step-nested scales. SN scales can be uniquely labelled by their step sizes and multiplicities. This scale is defined by the step signature and mapping (5 2 3) (10/9 16/15 81/80). The first mode listed is mode 2, and the second mode listed is mode -2, where the modes are listed in lexicological order.

The trivalent tetrachord just diatonic scales contained within the 10-note scale are not invariant under inversion, in fact, the scales, which clearly differ, are inversion of modes of each other. The just diatonic scale with 10/9 as the first step is available after the step pattern 1212121 of the first 10-note scale in its original mode. The scale found after the same step pattern of its inversion:
16/15 6/5 4/3 3/2 8/5 9/5 2/1
is a mode of the Ptolemaic sequence. The step pattern 1212121 is the symmetric mode of the maximally even sequence for 7 in 10. It can be generated by taking 3 fourths of the scale down from the tonic, and 3 fourths up.

The two just diatonic subsets of the 10-note scale have 3 large steps of 9/8, the major tone, 3 medium steps of 10/9 and two small steps of 16/15. ‘m’ and ‘s’ correspond to ‘L’ and ‘m’ of the 10-note scale, respectively, and ‘L’ corresponds to the addition of ‘L’ and ‘s’ (10/9 x 81/80 = 9/8). 

Let’s look at the two scales: 
10/9 5/4 4/3 3/2 5/3 15/8 2/1 – mLsLmLs and its inverse:
16/15 6/5 4/3 3/2 8/5 9/5 2/1 – sLmLsLm
In these modes they are in the form of disjunct tetrachordal scales, where the same steps in the same order reach tetrachords from 1/1 to 4/3 and from 3/2 to 2/1, separated by a 9/8 in the middle.
The definition of ‘tetrachordal’ I am using requires at least one mode of a scale to be expressible in this same form; with equivalent, disjunct tetrachords.
The tetrachord of the first scale is 10/9 5/4 4/3 – mLs, and the tetrachord of the second is 16/15 6/5 4/3 – sLm.

This improvisation was made using an axis-49 loaded into Pianoteq 5, using the default mapping. Try this out!

white square

From "Mikrojazz - Neue Expressionistische Musik"

Available on CD / Vinyl / Digital Download. 
A RareNoise Records Release. 

https://www.rarenoiserecords.com/gers...

"November" composed by Philipp Gerschlauer

Microtonal keyboard programmed by Philipp Gerschlauer

Philipp Gerschlauer, alto saxophone
David Fuze Fiuczynski, microtonal guitars
Jack DeJohnette, drums
Matthew Garrison, fretless bass
Giorgi Mikadze, microtonal keyboards

https://www.facebook.com/Gerschlauer/...
http://gerschlauermusic.com/home-eng....

LaMonte's Gamelan Jam (comp. Gerschlauer) Gerschlauer, Fiuczynski, DeJohnette, Garrison, Mikadze

The Stern Brocot Band perform Yak Butter. Inspired by Tajik Yak herder melodies, this piece is in a microtonal temperament called porcupine. It is played by Vassilis Angelis (drums), Maxime Canelli (guitar), Simon Holland ('cello), Andrew Milne (QWERTY). The engineering and mixing was done by Jim Hoyland at the Music Research Studio of The Open University, UK. You can watch the video version of this piece at http://www.youtube.com/watch?v=oNJr1YOOqF8.

Technical details: The tuning is period = 1196.9c, generator = 162.3c, scale = 1L, 6s MOS scale. Dynamic tonality synths were 2032 and TransFormSynth, played through Relayer (all software is freely available from www.dynamictonality.com).

Yak Butter (studio version) (2012)

Musically, I'm interested in the roiling interstices between the improvised and the composed, the unfamiliar and the familiar, the directed and the collaborated.

Yak Butter (studio version) (2012)

Andrew J Milne

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