Segunda entrega del dúo que musicalizó LA GRAN REUNIÓN. Alma, guitarra y cajón, la verdadera esencia de la tradición criolla.

Vete

This track is an example of using high prime numbers to create melody and harmony, to refute the claim that only prime numbers up to 37 / 211 / some arbitrary limit are useful for making music. This piece of music has a prime limit of 2499949 and the twin primes 2499949, 2499947 can be heard in sequence! To be honest, the focus was more on using higher prime numbers than making a decent sounding bit of music. So it sounds a bit out of tune! Sorry about that if you don’t like microtones! But I do. So here it is.

There are 2 bass lines which create a blues backing of fifths and major sixths in 5-limit JI. The overall structure is a twelve bar blues with one repetition and intro/outro.

There are 3 melody lines which meander about all over the place. Each bar is split into 12 chords, and the twelve bars are grouped into 5 sections of 48-24-24-24-24 beats. Each section starts and ends with a low-limit chord, mostly 5-limit triads or 3-limit fifths and octaves. Various interpolation methods are used to generate approximate intervals which are matched up to a big long list of prime numbers. The result is that higher primes are used as intermediate chords. I’m sure you will agree that the result is impressive! No two intermediate chords are likely to be tuned exactly the same under this scheme, demonstrating the virtually infinite flexibility of the chords in Just Intonation. (Note that some authors use Rational Intonation for when the primes get bigger than say around 41.)

Original sequencing and matching to prime numbers: Excel
CSV sequence file to WAV file: custom MATLAB/Octave script
Post-processing: Audacity

So a lot of primes were used. Which ones? I wrote an Octave script to interrogate the CSV and find the higher primes (over 1601). This was the result, a list of the 336 highest primes used:
2499949, 2499947, 2351963, 2344751, 2335183, 2322667, 2307073, 2288449, 2266591, 2241527, 2212633, 2180333
2144629, 2105231, 2061847, 2014471, 1963319, 1908703, 1849921, 1787033, 1719701, 1648567, 1258973, 1210427
1164749, 1122427, 1083031, 1045903, 1011947, 980773, 951791, 925447, 902191, 880907, 862399, 846037
831679, 819827, 809833, 801641, 795601, 791159, 788317, 786887, 522521, 521393, 517399, 516839
514201, 507901, 507329, 503317, 501029, 493853, 492029, 486349, 485417, 479263, 476299, 473197
(some omitted... 4000 char limit!)

The highest two primes (2499949, 2499947) are played in bar 5 in the top melody, as notes 2 and 3. They sound very similar!

Also, here are the fractions used for the first six bars of the top melody, which have units of Hertz (e.g. direct frequencies):
432/1, 1809/4, 1647/4, 1917/4, 1809/4, 1971/4, 1971/4, 2133/4, 2241/4, 2241/4, 2403/4, 2403/4
2403/4, 2619/4, 2619/4, 2727/4, 2727/4, 2727/4, 2889/4, 2781/4, 2889/4, 2943/4, 2943/4, 2943/4
3051/4, 3429/4, 3429/4, 3537/4, 3537/4, 3699/4, 3699/4, 3699/4, 3753/4, 4023/4, 4023/4, 4077/4
4077/4, 4239/4, 4401/4, 4239/4, 4509/4, 4509/4, 4671/4, 4671/4, 4671/4, 4833/4, 4833/4, 1296/1
1296/1, 22499541/16384, 22499523/16384, 21167667/16384, 21102759/16384, 21016647/16384, 20904003/16384, 20763657/16384, 20596041/16384, 20399319/16384, 20173743/16384, 19913697/16384
19622997/16384, 19301661/16384, 18947079/16384, 18556623/16384, 18130239/16384, 17669871/16384, 17178327/16384, 16649289/16384, 16083297/16384, 15477309/16384, 14837103/16384, 864/1

The highest prime 2499949 can be found here in the 22499541/16384 note.

No doubt this artistic endeavour will be used to spur interest in using higher primes directly in music. It has been fun - enjoy! Dave

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See also:
- https://arxiv.org/a/ryan_d_1 (arXiv) for a list of my academic paper pre-prints, including my writing on music theory and Just Intonation
- http://orcid.org/0000-0002-4785-9766 (ORC ID) for my academic profile
- https://www.linkedin.com/in/davidryan59 for my LinkedIn profile

Example of Prime Numbered Blues with JI prime limit of 2499949

This track has been created using an L-system, which is a type of fractal where large parts are comprised of smaller parts that look like reduced copies of the large parts.

As an example, a melody going up by a Just-Intonation perfect fifth (3/2 frequency ratio) could be comprised of three smaller copies going up 3/2, down 3/2, then up 3/2. This simple example would not be musically very interesting, however the idea is there.

In this particular track, the following mappings were used:

1 beat 1/1 --> 1/2 beat 4/3, then 1/8 beat 1/1, then 1/8 beat 9/8, then 1/4 beat 3/2 (inverted)
1 beat 3/2 --> 5/4, then 6/5 (both 1/2 beat)
1 beat 4/3 --> 10/9, then 6/5 (reversed)
1 beat 5/4 --> 9/8, then 10/9 (reversed)
1 beat 6/5 --> 4/3, then 10/9 (inverted)
1 beat 9/8 --> 1/1, then 9/8
1 beat 10/9 --> 1/1, then 10/9

Reversed means the smaller copy is played back in i) the reverse order and ii) the smaller copies are themselves reversed
Inverted means that the frequency shifts are inverted, e.g. f --> 1/f. So 10/9 inverted means ‘go down by 10/9’ or ‘shift by 9/10’

So an L-system melody has a set of melodies (in this case one each for 1/1, 3/2, 4/3, 5/4, 6/5, 9/8, 10/9) and each has its own set of ‘daughter’ melodies.

Each daughter has:
- an associated frequency shift
- a timescale, here they are all 1/2, 1/4 or 1/8 beat
- optional inversion and reversing operations, giving 4 possible orientations in total.

Rules include
- product of daughter frequency shifts must equal parent frequency shift
- sum of daughter timescales must equal parent timescale of 1 beat
- continue iterating until maximum timescale of (iterated) daughters is 1/2^n.

In this particular track, the three parts were:
Bass: reference freq 100 Hz, max timescale 1/32
Alto: ref freq 200 Hz, max timescale 1/64
Treble ref freq 400 Hz, max timescale 1/128

This gave a 3 part invention! Due to the fractal melody/harmony, the different parts were consonant with each other.

One extra option is pre-tuning or post-tuning.
- Pre-tuning means ‘take the note frequency to be from the start of the fractal block’
- Post-tuning means ‘take the note frequency to be from the end of the block’

In this track, post-tuning was used, which means that at the end of blocks the tuning tends to be in 1:2:4 (octaves) ratio. Pre-tuning could just as easily be used, meaning that blocks start off on octaves and change to other chords during each block.

Enjoy! Dave

--------------

See also:
- https://arxiv.org/a/ryan_d_1 (arXiv) for a list of my academic paper pre-prints, including my writing on music theory and Just Intonation
- http://orcid.org/0000-0002-4785-9766 (ORC ID) for my academic profile
- https://www.linkedin.com/in/davidryan59 for my LinkedIn profile

Example Just Intonation Fractal 3-part Invention

In The Air Tonight Drum Fill for 1 Hour 10 Minutes except it's tripled and one is played .1% faster and one is played .1% slower

In The Air Tonight Drum Fill for 1 hour 10 minutes at 99.9%, 100%, and 100.1% speed

heArt Ensemble with guest Claire Devlin (tenor sax): Guy Thouin (drums, percussion, composition), Félix-Antoine Hamel (tenor sax).

From the Basement #56: Milford Spirit

Audio examples from George Colligan's September 2010 lesson.

Ex. 5c

early demo mix

sh101, Casio FZ20m, modulars, cs80,727, most of this track is an Sh101 programmed&flexxed to fuk.
4x musicaid claptraps

syro

CIRCLONT12A Syro[ace].WAV

After several digital and physical releases in electronic genres under different aliases I have decided to go back to basics and record a host of heavily piano based organic music. This is the first track of the EP that is the first fruit of this labor, Music for Piano One: Beginnings. The tracks on this EP alternate between the peaceful, deliberately lo-fi, raw, noisy, minimal and pensive. Because they are vastly different from the other music I make I’m releasing them under the new alias Qaett.

Music for Piano One: Beginnings

Stream / download

This Too Will Be Swept Away

9.HYPER ATTILA

dark horse overlord acid+7

the first track from 'Cames Jook' by Goldefish and Alicia (@Aliciasteanson)

https://goldefish.bandcamp.com/album/cames-jook

Cover art by Ben Hall
Mastered by MatthewBentleyAudio (SPEKTRALSOUND)

9.HYPER ATTILA

Eric St-Laurent