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Audio phenomenon: Schroeder-phase complexes

Here's an audio phenomenon you should know about: Schroeder-phase complexes.

These are harmonic series which are designed so that their amplitude envelope is maximally flat. When you synthesise a harmonic series of partials, you know what frequencies you should use for the component sinewaves: F, 2F, 3F, 4F, etc. But what phase should you use?

Often we stick with a simple default such as every partial starts with zero phase. There's an issue with that, though, which can lead to issues in perceptual tests: the amplitude envelope, within one pitch period, is quite bumpy, because there are moments when the component phases all line up to produce strong amplitude. Sometimes this bumpiness leads to experimental confounds.

One thing you could do to work around this is use random phases, but adding this extra randomness into an experiment is usually not that desirable.

In 1970 Schroeder published a formula for choosing the phases so that the resulting waveform has a minimal crest factor, i.e. no big amplitude peaks. The formula is pretty simple but my blog doesn't render equations yet so see e.g. this paper.

Let me prove this to you directly: here I've synthesised the same harmonic sound with five different choices of phase. The top row, "sine-phase" and "cosine-phase" correspond to two versions of the default phase-aligned choice, and look how spiky they are:


In the middle is random phase, and at the bottom are two plots from Schroeder-phase. Please note that the y-axis has different scales in each plot - the waveforms each have the same energy, and the same Fourier-transform magnitudes, despite looking very different!

The reason that there are TWO Schroeder plots is because we have an option to flip the sign (time-reverse the waveform) while preserving the waveform characteristics. The shorthand label that people sometimes use is that one of these is "Schroeder-plus" and one is "Schroeder-minus".

BUT WAIT there's one weird thing I haven't shown you yet, and it pops out when you listen to the examples. These stimuli can be used to find frequency thresholds - at low frequency we can tell the difference, but at high frequency they sound identical. And the weirdest thing is when you listen to them at very low frequencies, they don't sound like static harmonic complexes at all (evenr though that's definitely how we generated them), they sound like otherworldly down- or up-chirps.

Listen to this audio file where I play a plus and a minus, at different frequencies. First at 300 Hz, then at 65 Hz, then 16 Hz, then 2 Hz. At first you'll hear two essentially identical tones, but then the differences become noticeable, and then overwhelming:

Download the wave file

It's a nice demonstration of the fact that any periodic signal can be conceived as a sum of stationary sinusoids - as in Fourier analysis. Here we synthesised a chirpy nonstationary-sounding (but periodic) signal, starting from scratch from the sinusoids.

My implementation is here as SuperCollider code, inspired by this paper: Phase effects on the perceived elevation of complex tones.

Tuesday 2nd February 2016 | sound | 1 Comment

The Tower Hamlets Local Plan

If you live or work in Tower Hamlets then please give them feedback on the "Local Plan" they're developing. It's a plan for the next 10-15 years of development in the borough.

So... what's the point of a Local Plan? In practice, it's a document which gives councils/developers/mayors the written "excuses" they need in order to do things or to block things. So the content of the Local Plan will indeed shape what happens.

Some comments from me:

  • Really important, in my opinion, are local markets for normal people. In TH we have great ones: Whitechapel Market, Roman Road Market, Chrisp Street Market, even the tiny little Globetown Market. These are all places where people can buy their fruit and veg and other stuff. They're great for local business, great for community cohesion, great for healthy eating. TH should preserve our local markets and make sure they thrive. There are a couple of threats to local markets: one is the commercial pressure from supermarkets and/or delivery services. Another risk coming from the overhyping of Shoreditch is the transformation of a market from a useful local place to a poncey market for expensive home decorations or what-have-you; could also be a risk of a market turning touristy I guess.
  • Cycling provision for all. The Cycle Superhighway is a bit controversial at the moment: lots of drivers on Mile End Road hate it, because of the congestion, but what they haven't realised is that the congestion is caused by the building works, not the cycle lanes themselves. Once it all settles down it'll be great for everyone. TH should maintain the great public cycle provision - the segregated cycle-lanes, the bike-hire stands. But also, the council needs to encourage all parts of society to take advantage of these things that the borough and the city have built. The facilities are mainly used by men, mainly within a certain age bracket, and I think also there are some ethnic groups that aren't benefitting too. So TH needs to keep up this provision but also do some outreach to get people using it.
  • Safeguard social housing - in fact safeguard all council / housing-association property. There are intense pressures on housing in London, and councils are generally put in a position where many of their options are shut off, but the current government is happy to say "Hey, why not sell of some of your stock, that'd help with cashflow." So there's a strong bias in favour of selling off the family silver. But in order to make sure ordinary working people can live in TH in future, the council and the housing associations need to maintain their position, at the very least, and ideally provide more social housing.
  • Improve the leisure walking routes in Tower Hamlets. There are some decent walking routes around here, e.g. from the Olympic Park down to Cody Dock, or along the Thames, but the provision is really quite fragmentary, and it'd be great to have a real consolidated network of pleasant right-of-way footpaths. For example, you can't currently walk all the way down the River Lea to the Thames. You can get some of the way but then you have to do a big diversion round the Tesco, and then a bit later a big diversion round the industrial estate. The supposed "Greenway" out of the Olympic Park has been blocked off by building work for many years, making it more theoretical than actual. Imagine how many people would reap the benefits if there were more consolidated leisure wlaking routes, taking advantage of our rivers and canals.
  • Some people complain about the number of tower blocks being built. I think it's more complicated than that - there are some excellent, really well thought-out new high rise areas in TH, while also there are some rush-job maximum-density useless blocks too. The council should ensure that developments are designed for living, providing amenities such as playgrounds and little parks, good public spaces and designated room for neighbourhood shops. And also ensure that private and social housing are mixed together, not divided into enclaves. In my opinion the St. Andrew's Hospital Redevelopment in Bromley-by-Bow is a great example of a well-designed modern housing area.
  • Planners need to remember that the Shoreditch hype is well over by now. How can they ensure that Shoreditch's new personality, after the trendy phase and then the gentrifying phase, works well over the next two decades? Retains some of its vibrancy? Frankly I don't know. But Shoreditch's trajectory over the next ten years is going to be completely different from the last ten years.

Also some things I found while reading around this topic:

  • There's a "Poplar Riverside Housing Zone" which is designated for housing development. "Future sites include Chrisp Street, Leamounth North and Aberfeldy" it says here. However I can't work out exactly where it is - they've not published a map. Does "riverside" mean by the Thames or by the Lea? I strongly suspect it's by the side of the Lea (approximately here) since that's the bit that's still basically industrial and not recently developed - can anyone confirm?
  • Looks like there are plans to build a "fashion hub" in Poplar.
  • There's some kind of Bromley-by-Bow Masterplan Supplementary Planning Document adopted in 2012 which relates to the area around Bromley-by-Bow. What does it imply? Well I don't know for sure, but: it labels some specific areas for regeneration, including the Stroudley Walk area and Empson Street; and it has a fair amount of development planned along the West bank of the river - including a "future green space" where Tesco's is! In fact, the other half of the area where Tesco's is is marked as "New District Centre: New town centre with mix of uses including retail, community uses, residential dwellings and commercial uses." Gosh. Oh and it also plans to fix one of my bugbears: the lack of connection between the West-bank towpath and Twelvetrees Crescent bridge (fixing that will really help join the riverside walking routes up).

But anyway, like I said, give them feedback on the Local Plan.

Saturday 30th January 2016 | politics | Permalink / Comment

An executive summary of Islam in Britain

Just finished this really useful little book: "Medina in Birmingham, Najaf in Brent: Inside British Islam" by Innes Bowen. It could well be subtitled "An executive summary of Islam in Britain", because that's exactly what it feels like - a brief, breezy and dispassionate summary of the main Muslim groups in the UK, what they believe, how they interact with the world, etc.

Very handy reading, if you're a non-Muslim British person like me who might be wondering: the Muslims in my neighbourhood, are they sunni or shia? Does it matter? How do they relate to the various Muslim groups that are making the news these days? Which ones dress in special ways, and how significant is it? - All those naive questions that you can't just come out and ask.

All kinds of interesting stuff comes up while answering these questions. For example I learnt about the Tablighi Jamaat and why they wanted to build the "mega-mosque" that has been back and forth in the news trying to get planning permission. I learnt which groups have a voice in the Muslim Council of Britain. And even though the book doesn't spend much time on women's issues, it gives lots of titbits about different groups' conventions on veiling, staying in the house, marriage, and mosque provision - so it gives me some "local" insight to complement this other reading on veiling practices.

As in that other book, one thing that might surprise you is that some seemingly "traditional" things (like clothing practices) are borne of quite modern movements within Islam; really, you realise that "traditional" vs "modern" is not a particuarly helpful way to distinguish different strands of Islam practiced in Britain today.

Sunday 10th January 2016 | books | Permalink / Comment

Kale and rosemary flatbread

Kale and rosemary flatbread. What I particularly like about this flatbread is that the kale baked in the oven goes crispy like fried seaweed. I had it as a main course with a bit of rocket and some manchego cheese. It could also be a good accompaniment, maybe an accompaniment to something meaty.

Serves 2. It's derived from a recipe from "Crumb" by Roby Tandoh.

  • 250g strong white flour
  • 1 tsp instant dried yeast
  • 1/2 tsp salt
  • a twist of black pepper
  • 175ml lukewarm water
  • a few (6? 10?) tines of fresh rosemary
  • 4 tbsp olive oil
  • 150g kale, stalks removed, and shredded

Combine the flour, salt, pepper and yeast in a large bowl. Make a well in the middle and add the warm water. Mix with a fork, then when that gets difficult add 1 tbsp of the olive oil and rosemary, and mix with one hand.

Knead it for 10 minutes. You might be able to do this in the bowl or it might be easier to tip it out onto a clean surface. You might need to sprinkle a bit more flour on. It should become elastic and less sticky.

Now cover the dough and let it rise for 30-60 minutes in a warm place. Meanwhile, blanche the kale: bring a pan of water to the boil and plunge the kale in. Boil it quickly for 1 minute, then immediately drain it and run cold water over it to stop it from cooking any further. Now you need to get it as dry as you can, firstly by draining it then by pressing it gently.

Knead just under half of the kale into the risen dough. It'll be a little tricky, due to the residual moisture on the leaves, but there's no need to worry about it being perfect.

Preheat a fan oven to 170C. Using a rolling pin and a floured surface, roll out the dough and then roll/hand-stretch it into a kind of A4 shape, quite thin, and put it onto a lightly floured baking tray. Put the remaining kale over the top, pressing it down a bit so that it'll stick in. Drizzle plenty of olive oil over the top and bake for 20 minutes.

Sunday 10th January 2016 | recipes | Permalink / Comment

Poverty: demolish sink estates or not?

David Cameron wrote an article today saying that knocking down poor people's homes is how to make their lives better. ("David Cameron vows to 'blitz' poverty by demolishing UK's worst sink estates").

There's a short version of my response to this: go and read Anne Power who's studied housing and regeneration a lot, and has concrete recommendations for the best way to handle all this stuff. Read this article: "Housing and sustainability: demolition or refurbishment?"

I was undecided about all this stuff in 2014 when I went to see the Carpenters Estate protests. If you're not involved, it sort of sounds like a good idea. "Ooh those scary estates. If we knock them down and replace them with shinier ones, that's the neatest way to fix the situation up, and the residents can come back and live in them so they won't be any worse off."

But then you go down to the estates and meet people, and you read about how these regenerations happen in reality, and you realise it's not as neat as that. Firstly, in modern times regeneration usually involves selling off a fraction of the estate for private development, and the community doesn't really get to be rehoused back together, many get scattered to random locations over which they have no choice. Community cohesion is lost, i.e. part of the social fabric that keeps everyone safe. Secondly, demolition has unhelpful side-effects on the area around it (house prices, antisocial stuff, disrepair, local services leaving). Thirdly, there are alternatives to demolition (renovation, infill building) which avoid many of these downsides, are more sustainable, and are good for the local economy because local small-scale builders can do them.

Cameron said three out of four rioters in 2011 came from sink estates. "The riots of 2011 didn’t emerge from within terraced streets or low-rise apartment buildings. The rioters came overwhelmingly from these postwar estates. That’s not a coincidence," he wrote.

David Cameron, your logical fallacy is: False Cause. The people he's talking about are poor and disenfranchised, and that's the common cause of both things. It's the cause of living in the less popular estates, and it's an important cause of the rioting. It's not the shape of the buildings which caused the riots!

The current UK government is acting from a position of strength, and they are really taking their opportunity to make bold moves in the directions they want. Putting money into improving housing can be a good thing - the biggest risk I see is that this initiative will end up pushing poor people out of the way and fragmenting their communities. We can do it better. Read this article: "Housing and sustainability: demolition or refurbishment?"

Sunday 10th January 2016 | politics | Permalink / Comment

Poached thai-style sea bass

Poached thai-style sea bass - a handy everyday recipe, easy to do, healthy and fresh, whenever you see a nice piece of sea bass in the shop. It takes less than ten minutes. All of the flavourings are optional really but most of them can be kept in your store cupboard.

These amounts are to serve one.

  • 1 fillet of sea bass
  • 1 portion dried noodles
  • Flavourings:
    • 2 spring onions
    • 1 lemongrass stalk
    • 1/2 a chilli
    • a piece of root ginger (maybe 2 cm cubed?)
    • 1 or 2 lime leaves
    • a dash of fish sauce (or if you don't have that then a dash of light soy sauce or worcestershire sauce will add a bit of depth to compensate)
  • to serve: a small amount of fresh coriander or parsley

Boil a kettle.

Meanwhile chop things up: the spring onions into ~1mm slices, the chilli into ~1mm slices, the root ginger into fine slices, and chop the parsley. Don't chop the lemongrass, but bruise it (bash it with the heel of the knife a bit). Don't chop the lime leaves.

Put all the flavourings (not the coriander/parsley) into a pan with a small-soup-portion of boiled water and bring it to the boil. Add the noodles, then add the seabass so it sits on top of them (it should still be submerged though). No need to stir anything.

Turn the heat right down and put a lid on. Let it poach for about 5 minutes.

At the end, ladle the whole lot into a soup dish, ideally keeping the fish in one piece sitting on top. Sprinkle the coriander/parsley on.

Sunday 3rd January 2016 | recipes | Permalink / Comment
Mushy peas three-way showdown (Monday 14th December 2015)
Dry-fried paneer (Thursday 26th November 2015)
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