The Microtonal Thread

General
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I just now noticed this thread; I didn’t realize it mentions me (albeit on a different forum).

I’ll start by sharing a blog post about an unequal temperament I devised: http://prairieboxes.blogspot.com/2019/08/a-cosine-derived-well-temperament.html

I’m glad this was found to be interesting or useful outside its initial context! I have some other posts on that forum that are relevant. (See below; they are in context in this reply.)

I have contributed over there a bit (in the past year), and I got that impression a bit. Also that some users are discovering this stuff on their own terms, without a formal mathematical foundation and using the site to document their investigations (using their own terms). This isn’t bad in itself, but not particularly helpful if you’re just looking for a reference.

A little number theory would go a long way in making more sense of it.

There’s a lot of good stuff on Kraig Grady’s anaphoria. He has the archives of Erv Wilson.
He’s also a main contributor to the journal Xenharmonikon.

I have made use of Grady’s “Centaur” 7-limit just tuning. Here’s something I did for the Disquiet Junto earlier this year:

Some monophonic synths use a resistor ladder to develop the voltages. The tolerance of these resistors is one source of tuning error.

Some electronic organs and synths use a “Top Octave Generator” which approximates equal temperament with rationals that can be implemented in a counter circuit.

I discussed both of these (and emulating them) on the Sequential forum here: https://forum.sequential.com/index.php/topic,3487.msg37298.html#msg37298

If anyone has interest in the Scala files for these, let me know. The files linked on the post are MTS formatted MIDI SysEx files.

In the days before Melodyne, Joe Monzo did a nice blues microtonal analysis: A Microtonal Analysis of Robert Johnson’s “Drunken Hearted Man”.

I like the term “mesotonal” (I think coined by Kraig Grady) for scales that are not traditional 12TET, just intonations, or related temperaments. He applies it for scales that still have about 12 tones per octave, reserving “microtonal” for scales with much more than 12. (By extension, “macrotonal” describes scales with much less than 12 tones per octave.)

Of course the term “Xenharmonic” is apt for scales that don’t relate closely to known scales used by Earth cultures.

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The best and only microtonal pop song I know of. Are there others?
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I always have trouble telling whether something is “pop” but these are at least examples of vocal music using some non-12EDO scales:

Nadah El Shazly (Arabic alternative music):

Brendan Byrnes’s Neutral Paradise (microtonal 80’s synthpop pastische):

Elaine Walker (I don’t know what genre this would be but the tuning is Bohlen-Pierce):

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Thanks for that! I wonder if the scale is traditional, something innovated from the traditional arabic 24-tone set, or something else.

I prefer Byrnes’ (mostly) instrumental album Micropangaea. This is my favorite track.

The “liner notes” used to be on micropangaea.com, but now you have to get them from the Wayback Machine:

This piece was written for 6 standard fretted guitars tuned to notes of 17 EDO. Since perfect 4ths and 5ths are only a few cents off the ones found in 12 EDO, the guitars could be played on frets 5, 7,12, and 17 and always remain very close to the sound and tuning of 17EDO if not perfectly accurate. Most of the guitar parts are interlocking and hocketed melodies, with most of the harmonic accompaniment and bass handled by an electronic backing track. In order to minimize confusion while composing the piece, I put colored stickers representing each guitar pair (guitar parts were mostly doubled) on a keyboard to keep track of which notes were playable by which guitar.

Even though the hocketing was a side-effect, I think it ends up being a big part of the charm of the track.

I like that her tracks on Bandcamp always state which tuning is in use:

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I don’t know what exact scale it is but Nadah and that scene of music (people like Tamer Abu Ghazaleh, Maurice Louca, etc.) seem pretty pragmatic about traditional scales. You’ll often hear songs bringing together fretless instruments obviously playing quartertones with regular guitars and synths. How she uses the scales is also non-traditional. From my rudimentary knowledge of it, maqam music doesn’t really use harmonies but that song I linked ended with some really nice vocal harmonies.
It’s interesting stuff I’m trying to learn more about.

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For those interested in Richard D. James / Aphex Twin, here’s an extensive interview where he talks about his own exploration of microtonal music, and also his contribution in designing the Korg Monologue to include microtonal programming features:

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managed to work a microtonal performance thing into a history class final this week

bayati64.amxd (1.2 MB)

that’s a lil simple 64 grid app for playing back notes in an Arabic scale (maqam bayati). it actually uses midi (in max for live) - it just sends a bend for the one quarter tone in the scale so if u set yr synth to mono and pitch bend range to a semitone you’ll get the 24tet stuff

anyway just one 7-note scale so not getting all the harmonic variety you’d find in arabic music - but it’s got a lil extra something

nice resource for arabic music theory I found: http://maqamworld.com/en/index.php

&& bonus video of stuff being done properly cuz I got really into arabic music while I was working on this !

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I just saw something on CDM I think showing a microtonal device in Bitwig… I’m way too long devoted to Ableton to be attracted to Bitwig but it would be cool if there was a way to get Live devices to respond to microtuning…

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Playing around with Just Intonation for the first time thanks to Crow and Just Friends which allows me to enter numerator and denominator values for each oscillator. But I’m hitting a road bump in my understanding of the difference between Equal Temperament and Just Intonation.

For example, I want try tuning JF to 5-edo, which as far as I understand is dividing an octave into 5 equally spaced notes. Therefore, I figured I would enter the following as the values for the osciallators:

1: 1/1
2: 6/5
3: 7/5
4: 8/5
5: 9/5
6: 2/1

But when I compare the output to a 5-edo reference file online they don’t sound alike. When I explore a little more I find this page on the Xen Wiki which has a chart showing ‘JI Intervals approximated by 5ed2’ which states that, for example, the fourth note in 5-edo would be 960 cents (4/5) but the equivalent JI values of 9/5 would be 1017.6 cents.

So, I’m confused: why wouldn’t 9/5 be equal to 960 cents? Clearly I’m missing something here.

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The “equal” part of “equal division of the octave” refers to ratios between notes. Your values are linearly equally spaced (you’re adding the same value each time), but the interval (ratio) between note 3 and note 2 is (7/5)/(6/5) = 7/6, between note 4 and 3 is 8/7, etc.
Since perception of pitch is logarithmic, equal spacing needs to be logarithmic: multiplying by a constant factor, rather than adding. The interval of an octave is usually expected to be exactly 2, so “dividing” the octave n times means choosing a ratio that, multiplied by itself n times, gives you 2. Perhaps counterintuitively, this operation isn’t actually division, it’s taking the nth root.

In 5-edo, the step between notes is a factor of 2^(1/5), which is equivalent to 240 cents. Cents, like decibels, are inherently logarithmic: 1 cent = 2^(1/1200) but 100 cents = 2^(100/1200) = 2^(1/12), etc.

1: 2^(0/5) = 1.0
2: 2^(1/5) ≈ 1.1487
3: 2^(2/5) ≈ 1.3195
4: 2^(3/5) ≈ 1.5157
5: 2^(4/5) ≈ 1.7411
6: 2^(5/5) = 2.0

I’m not an expert but I think it’s not too bold to say that one of the arguments in favor of just intonation is avoiding irrational numbers like these… so if you’re setting the oscillators in terms of ratios of whole numbers, it’s never going to be 5-edo exactly. That’s why that chart gives you approximations that get reasonably close while using small integers.

Hope this helps and is not just more confusing.

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It helps a lot, many thanks for the explanation!

This was the big eye opener for me:

which explains this:

I guess the part that threw me off was when using Scale Workshop the increase in cents is linear (0, 240, 480, 720, 960, 1200), but I wasn’t looking at the frequency values which are clearly logarithmically increasing.

Thanks for taking the time to explain! Having a lot of fun exploring this stuff. Now the hard part seems to be picking a xenharmonic scale to explore, I could keep swapping them out forever, haha!

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Pardon my dumb newbie question: how would one “put” such a scale into an Arc or a Grid? I suppose I would need some sort of voltage calculator and then define absolute voltages. Has anyone done that? Thanks for any hints.

LC

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Teletype would do just fine for this if you’re working with control voltage!

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I have been rinsing this album since yesterday. Thanks for the recommendation, LOVING IT!

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Brendan also did a tutorial on microtonal music based on one of the songs off that album:


It’s pretty interesting to hear his thought process when writing and especially the tools he uses to retune everything.
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Nice, thanks! Some evening watching for me.

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o_C scales into the Teletype, such a delight!
And so useful.
Spools of gratitude~~~

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Can you describe this more?

Thanks!

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@eblomquist not sure if your request was directed at me but i was referring to the scale-conversion that @karol gifted us

it’s super nice!

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Thanks! I’m feeling the slow but inescapable approach of a Teletype…

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