↬ Twenty-three – 03: Scales, Tuning, Typography

Hi, I’m Rudiger Meyer and this is my monthly newsletter covering what I’ve been up to and what’s been catching my attention.

Besides having being knocked out for a week by yet another bout of Covid, I’ve been spending a lot of time with my nose buried in Audulus.

As I mentioned in my previous letter I’d gotten busy with putting together scales and tunings for some Audulus quantizer tiles/modules.

Reading up about Arabic tunings while brushing up my knowledge while working on the Scales tile, I came across a description of a division of the octave into 17 (unequal) steps that was apparently the basis of Arabic music theory before being superseded by the modern division of 24 steps. 17 steps could be played on the common 12-key-to-the-octave keyboard that we know today if the black keys were split in two, and, having seen some historical examples such as the Archicembalo, that gave me the idea of using a toggle to create a virtual split of the black keys (where one selects either the higher or lower part of the split) and keep the Tuning tile compatible with MIDI keyboards and the Scales tile.

I did’t know very much about the details of the 17-step Arabic tuning, but it was apparently based on perfect Pythagorean 4ths and 5ths, so instead of the common practice creating a chromatic Pythagorean scale via six perfect fifths above the starting note, and five fifths below, I took the ratios for what one would get when extending to 11 pure fifths above and below, so as to create a split on the ‘black keys’. For this experiment it was only the black keys that were affected by the split. The ‘white’ notes remained unaffected by the toggle and retained their basic Pythagorean tuning.

(Although it might at first seem counterintuitive, I assigned the 5ths calculated down from the root to the # option of the toggle since they correspond more closely to a natural ‘just’ tuning of a Major third, and conversely the 5ths calculated up from the root were assigned to the ‘b’ option of the toggle: I.e. selecting flat (‘b’) will makes for better tuning of minor triads, and sharp (#) provides better tuning for major harmonies.)

Having completed the 17-note version, I realised that if the split was extended to the ‘white’ notes as well, with only the root and the fifth remaining constant, that this would provide a possible version of the 22-note-per-octave Indian Shruti system.

In this case only the root and fifth are constant – all the other notes, both ‘black’ and ‘white’ have two values, selected via the b/# toggle. (Upper/Lower = successive Pythagorean perfect (3:2) 5ths calculated up/down from the root note.) In this case the chromatic ordering is adhered to – the series of ‘lower’ notes is accessed via the ‘b’ toggle and the upper via ‘#’. (Though, as with the 17uDO setting, this upper series gives better minor thirds and lower better major thirds). The toggle can be shifted via a modulation input, potentially via a MIDI controller to enable easily shifting from one adjacent note to another.

I then discovered Erv Wilson’s tunings for the 17-note Persian scale, and so included them alongside my 17uDO (Pythagorean) version. Rather than the ‘black notes’ it turns out that it’s the seconds and thirds (i.e. also the sixths and sevenths) along with the aug. 4th/dim. 5th in the Persian scale that have higher and lower versions of the notes. As with my 17uDO and the 22 Shruti scales, the higher or lower of the ‘split’ notes are selected via the (modulatable) toggle.

I concluded that not all of the North Indian Raga-scales listed by Erv (and included in the Wilsonic app) were available – unless one shifted between higher and lower parts of the split mid-scale, and made demos of 2 scales that I found were possible without a shift.

I subsequently discovered however that Erv Wilson had put together a “12-fret” version of the Persian 17 scale in which most of the notes are taken from the lower split, but with some from the higher, in this way enabling all of the 25 North-Indian Raga-scales he lists, to be mapped to them. Only the 9th degree of the scale is ‘split’ and needs to be raised for 4 of the 25 Raga-scales. (See the final pages of this document)

I added an extra tuning following Erv’s scheme, with the toggle raising the 9th. I also added a special scales tile dedicated to the 25 Raga-scales. It includes an output that, when connected to the toggle input of the Tunings tile, automatically raises the 9th degree of the 4 affected scales.

Erv’s mapping of the scales demonstrates nicely how the various seven-note Raga-scales pull from the more complex pool of 17 notes, without ever employing the notes directly adjacent to each other (separated by the interval of 81/80) The same applies to the 22 steps of the Indian system.

It’s been a fun journey in which I’ve come, gradually through my own stumblings, step by step as I’ve tried to implement these tuning systems in Audulus, to a better understanding of the Persian and Indian systems. Erv Wilson sums-up with some good insights:

1. The Pythagorean Diatonic, with true Fifths, modulated through 6 keys gives a 12-tone genus.
2. Meantone 12 retains these six keys but seeks good thirds at the expense of the Fifths.
3. However when the Just Diatonic, having both true Thirds and true Fifths, is modulated through the same six keys a 17-tone genus results.
   —Erv Wilson (1980) Some Basic Patterns Underlying Genus 12 & 17 

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I’ve also added a Bagpipe tuning, based on McDonald Wilson’s tuning for Highland Pipes, based on the harmonics of the drones, as found in one of Erv Wilson’s documents. The interesting thing with this tuning, in which the 3rd and 6th of the scale are tuned to the 13th harmonic of the bagpipe drones, is that it, being around 40 cents sharper than a tempered minor third, approaches a neutral third.

From the Wikipedia article on the Highland bagpipe:

According to Forsyth (1935) the C and F holes were traditionally bored exactly midway between those for B and D and those for E and G, respectively, resulting in approximately a quarter-tone difference from just intonation, somewhat like a “blue” note in jazz.

Today, however, the notes of the chanter are usually tuned in just intonation to the Mixolydian scale, with the G tuned to the harmonic seventh which is significantly flatter than the just minor seventh or the equal temperament minor seventh.

In my version the toggle activates the ‘neutral third’ version, with a standard justly intoned Mixolydian scale as the default. I chose to stick to the slightly higher 7th (16:9) – equivalent to 2 fourths, rather than the 7:4 ‘natural’ seventh, as it seems to lend itself better to playing melodies. (It can easily be shifted out internally though.)

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I also updated my Hordijk Harmonic Oscillator, making use of the resampling functionality now available in Audulus 4 to achieve a definition in the waveforms that wasn’t possible before. But that’s another story…

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One interesting aspect of experimenting with all these temperaments and tunings, is that (perhaps with the exception of the neutral third scales) they don’t necessarily sound all the ‘exotic’. Comparing the ‘purer’ tunings with equal temperament is not necessarily earth-shattering, but they certainly provide some more subtly beautiful colours.

In this respect I got to think of Frank Chimero’s blog posts on how typefaces can alter the overall feel of a (web) page/text. How the design of seemingly very similar letters accumulate into the feel of a typeface when larger swaths of text are present. The posts are unfortunately no longer available on his site, but they can be acesssed via the Web Archive:

Another aspect is how many of these fonts are modern ‘interpretations’ of classic typefaces. Söhne, Kris Sowersby’s take on Akzidenz-Grotesk (the memory of Akzidenz-Grotesk framed through the reality of Helvetica), is a good example, and as Frank unfolds in his posts, each of these ‘versions’ lend a character the the text one sets with them, a character that might be hard to distinguish when comparing a single letter at a time, but becomes more clearly apparent when viewing larger expanses of text. There’s an incredible amount of attention to detail, and that’s something that one can ‘feel’ even without necessarily consciously ‘pinpointing’ those details while reading.

I’m wondering how the same might apply to music.

Modern ‘re-interpretations’ of these well-known (historical) tunings and temperaments?

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A short video (dating back to 2006) of Stephen James Taylor playing an excerpt of one of his compositions on an Erv Wilson Generalized Keyboard was posted on Marcus Hobb’s Discord. The music doesn’t sound particularly radical – somewhat impressionistic, but there’s been something about it that caught my ear. Something about how the pure tunings alter the MIDI woodwind sounds, make the melodies and harmonies that are passed through them sound more ‘real’? As if the nodes of the tubes somehow become more apparent, or am I simply imagining that?

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Music: Unseen Worlds (re)released another gem: Daytime Viewing by Jacqueline Humbert & David Rosenboom. Performers that worked with Robert Ashley, and very much that kind of world. David Rosenboom features in Desert Plants, the Walter Zimmerman book of interviews with American composers conducted in the mod-70s. Rosenboom is on about his experiments with using brainwaves to interact with synthesizers, and his work in the field with Don Buchla. On Daytime Viewing he used another instrument developed wit Buchla – the rare Touché, with a (unusual for Buchla) regular keyboard and all. I’ve been fascinated by the sound of it. This track, for example.

All the best,
↬ Rudiger