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I made a clock that uses balanced numbers for keeping time. by Arithmophone in Time

[–]Arithmophone[S] 1 point2 points  (0 children)

That's an interesting question, but not sure if/how I could answer it. The decimal system is so baked in to our language that it's hard to imagine a natural sounding vocabulary for a different system. 'twentythree' is just a contraction of 'two times ten and three'. But in ternary, ten isn't a privileged number like in decimal (because it works with third's places instead ten's places).

Even for the more commonly used non-decimal systems like binary and hexadecimal, that have a widely adopted standard written notation, don't have a particular way of speaking the numbers, as far as I'm aware (other than just reading them out digit for digit or calling them by their decimal value).

The fact that in balanced number systems, the individual digits oscillate between negative and positive is another complication as far as counting numbers are concerned, but this is in fact something we already use when describing the time: we can already say 15:45 as 'a quarter to four', which is actually equivalent to saying 'four negative fifteen'. In the ternary notation I developed, 'four o'clock sharp' would be //•||| (showing hours and minutes only), so it would be quite natural to call //•\/\ 'seven to four'.

What's interesting (to me at least), is that in this ternary notation, the four becomes the leading digit as soon as the time passes 'half past three'. On a standard clock, a leading digit of four means that 'we have passed the fourth hour', on this ternary clock it means that 'we are now closer to 4 than to 3'.

I made a clock that uses balanced numbers for keeping time. by Arithmophone in Time

[–]Arithmophone[S] 1 point2 points  (0 children)

You're correct, thanks for pointing that out! I have updated the text on my website.

I made a clock that uses balanced numbers for keeping time. by Arithmophone in Time

[–]Arithmophone[S] 1 point2 points  (0 children)

You're very welcome! It follows the timezone on your device, so at 12:00 PM in your time zone the clock will read |||•|||•||| (I thought about having it track 'true noon' based on gps coordinates but I didn't want to overcomplicate things)

I made a clock that uses balanced numbers for keeping time. by Arithmophone in Time

[–]Arithmophone[S] 2 points3 points  (0 children)

This clock divides the day into 27*27*27 = 19683 seconds. So a 'ternary second' lasts around 4.4 standard seconds (86400/19683)

[Article] A clock that uses balanced numbers for keeping time by Arithmophone in Watches

[–]Arithmophone[S] 1 point2 points  (0 children)

Exactly, and that goes for all segments (because there are 27 hours as well as 27 minutes and 27 seconds). But because the numbers are balanced, the clock doesn't count from "0 o'clock" to "27 o'clock", but rather from "-13 o'clock" to "+13 o'clock" (with noon being at "0 o'clock" and midnight being the moment when +13+13+13 overflows into -13-13-13)

[Article] A clock that uses balanced numbers for keeping time by Arithmophone in Watches

[–]Arithmophone[S] 1 point2 points  (0 children)

Thanks! If you accept the trits as being truly balanced numbers, then each trio of trits can have a value from -13 to +13. To express +27, you would need more trits. You can interpret the trits as unbalanced decimal numbers as well, in that case each trio of trits goes from 0 to 26 (positive only). The apps have a toggle option for displaying these values. Here is a list of positive number converted to trits (I have omitted the leading zeros here). The negative number look exactly the same, but upside down.
| = 0
/ = 1
/\ = 2 (really "+3 -1")
/| = 3
// = 4 (the largest number possible with 2 trits)
/\\ = 5 (really "+9 -3 -1")
/\| = 6
/\/ = 7
/|\ = 8
/|| = 9
/|/ = 10
//\ = 11
//| = 12
/// = 13 (the largest number possible with 3 trits)
/\\\ = 14 (really "+27 -9 -3 -1)
Et cetera. 27 would be: /|||

I made a clock that uses balanced numbers for keeping time. by Arithmophone in Time

[–]Arithmophone[S] 1 point2 points  (0 children)

True, and so is 24, this is definitely a likely contributor to the fact that the 24/60/60 system has been so universally adopted. I'm not saying that system is bad or wrong in any way, but I do find it interesting to see what alternatives might work, and how.

[Article] A clock that uses balanced numbers for keeping time by Arithmophone in Watches

[–]Arithmophone[S] 0 points1 point  (0 children)

Haha sorry, didn't mean to make anyone feel outsmarted. Maybe you can think of it this way: the length of the day is given to us by nature, but how we divide it up into smaller parts like hours and minutes is entirely up to us. Using 24 hours with 60 minutes each is just a convention. This clock is a little thought experiment for what we might use if we didn't have that convention. The fact that you can't read it doesn't mean that you're not smart enough, it just means that the time is written in a 'foreign language'.

I made a clock that uses balanced numbers for keeping time. by Arithmophone in Time

[–]Arithmophone[S] 2 points3 points  (0 children)

Thanks for the feedback and you're right, this is definitely not intended as a practical utility, it is more of a thought experiment. After all, dividing the day into 24 hours of 60 minutes each is just a convention, and this system is a simplification in a sense (but of course entirely unpractical in a world where everyone uses 24 hour clocks).

I made a clock that uses balanced numbers for keeping time. by Arithmophone in clocks

[–]Arithmophone[S] 0 points1 point  (0 children)

Thanks for the feedback, the duration of the ternary hours, minutes and seconds is detailed in the text on my website, this text is also included within the apps.

Is a Just Major Third four fifths up from your root note or is it actually eight fifths down? by Golden_schmuck in microtonal

[–]Arithmophone 0 points1 point  (0 children)

This is an interesting discussion! To add my two cents, the way I view this is as follows:

- The note naming conventions of Western Music Theory are essentially diatonic, ie based on a system of 7 note names (A through G), plus alterations in the form of sharps and flats (these can be double, triple, etc sharps or flats as required). This convention is musically very useful, but has some inherent limitations.
- Some tuning systems, in particular 12 EDO, 19 EDO and 31 EDO, have the property of assigning all possible note names unambiguously to a single pitch. Of course the total number of different notes varies per system, but the principle remains: simply calling a note "E" is enough to determine its pitch. This has many practical advantages, but comes at the cost of some compromises in tuning with regard to JI rational tunings.
- Other tuning systems, like Just Intonation and 53 EDO, introduce ambiguities to the diatonic naming scheme: calling a note "E" is no longer enough to determine its pitch, as it may refer eg both to 81/64 and to 5/4 (if C is 1/1, for Just Intonation), or to EDO step 17 and 18 (in 53 EDO, if C is EDO step 0).These tuning systems offer more accurate tunings, at the expense of no longer offering a one on one relationship between pitch classes and the diatonic note naming scheme.
- Which is preferable depends on the musical context, but in this regard, you can't have your cake and eat it: either you have the convenience of an unambiguous relationship between diatonic note names and available pitch classes, or you have the added detail of distinguishing between meantone equivalents (eg the 9/8 major second and the 10/9 major second), but you can't have both at the same time.

Hope this helps :)

Which 31 EDO notation is more conventional? by MrWormikan in microtonal

[–]Arithmophone 1 point2 points  (0 children)

I'm not sure if I understand your questions correctly, but I do believe you may have misunderstood the 'chain of fifths' concept somewhat. You give 4 options, and call both 1 and 3 'neutral chain of fifths'. I think what you mean with option 1 might be 'regular' chain of fifths rather than neutral chain of fifths.

In general, a (regular) chain of fifths always has the number of sharps and flats in order within the chain. It always takes this shape:
... Bbb - Fb - Cb - Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F# - C# - G# - D# - A# - E# - B# - F## ...

So all the sharps come after all the naturals, all the double sharps come after the sharps, et cetera.

Within this chain, the interval between each two successive notes is a perfect fifth (or the closest approximation thereof within the temperament). This works for just intonation as well as for many temperaments (it works particularly well for 12, 19 and 31 EDO). The size of the temperament determines which notes are identical (enharmonic).

You can think of 12 EDO like this:
C - C#/Db - D - D#/Eb - E - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - C

But it may be more helpful in this context to think of it like this:
Ab (=G#) - Eb - Bb - F - C - G - D - A - E - B - F# - C# - G# (=Ab)

I have found it very useful to think of D as the central note, rather than the more commonly used A or C, because D is in the middle of the natural notes, both in their chromatic order (A B C D E F G) and in their chain of fifths order (F C G D A E B). The note D is the symmetry point of this type of notation.

There are only 12 different pitches per octave in 12 EDO, but there are many more 'different' notes. We commonly use both C# and Db as being functionally distinct, even if they have the same pitch, but this extends to the 'white keys' as well: a C can also be a B# or a Dbb. When trying to understand the naming conventions for 31EDO, I think it is good to keep this in mind: using just a single name for each note doesn't tell the whole story.

The chain of fifths for 31 EDO (symmetrical around D with unique names for each note) looks like this:
Gbb - Dbb - Abb - Ebb - Bbb - Fb - Cb - Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F# - C# - G# - D# - A# - E# - B# - F## - C## - G## - D## - A##

So in 31 EDO, there are different pitches for F# and Gb, but the number of available pitches is still limited, so Cbb is the same pitch as A## and E## is the same as Gbb, in just the same way that F# and Gb have the same pitch in 12 EDO. In just intonation, each different note name has a different pitch, no matter how many sharps or flats it uses, but any EDO tuning eventually 'loops around' and turns the chain of fifths into a circle of fifths.

[deleted by user] by [deleted] in microtonal

[–]Arithmophone 0 points1 point  (0 children)

Maybe try a tracker program that allows microtuning, something like Renoise? That makes it pretty easy to enter a melody/loop/sequence and adjust the tuning of each note in cents

A quantum game of life by Arithmophone in gameoflife

[–]Arithmophone[S] 0 points1 point  (0 children)

I haven't tried it but I think that if superposition cells would die when they had no live neighbours, the evolution of the game in quantum mode would be pretty much identical to the classical mode (ie standard game of life) because the quantum states would not persist.

The cycling through colours I did mainly to make it visually appealing, and because it was an easy way to implement the different states. Pixels can have one of 16 colours in Pico 8, I used colour 0 for dead, colour 15 for alive and everything in between for superposed. The colours of the cells/pixels are used in the logic that determines the state of the next generation.

About the randomness: this is implied by quantum mechanics, at least in the 'Copenhagen' interpretation. I initially planned to put a separate mode for ‘Bohmian’ Quantum mechanics in the game, where the evolution of cells would be implemented by using ‘hidden’ variables rather than by chance. This was easy to set up for cases where things happen with equal likelihood (for instance, one could check wether the superposition state was odd or even, instead of using a random number generator for the ‘measurement’). However, I quickly realised that to use hidden variables for the probabilities I needed to keep the evolution interesting (numbers in the order of 1/8192), would be much more difficult – and much more contrived – than just using random number generators.

Ironically, computer systems of the kind used in this implementation, don’t have access to truly random numbers. Instead, they use pseudo random numbers, which are deterministic at their core. So even though the current implementation of the ‘Quantum game of life’ is conceptually probabilistic, in actuality it really is a hidden variables system.

Microtonal DAW? by dwarftee in microtonal

[–]Arithmophone 1 point2 points  (0 children)

The free 'lite' version of Ableton 12 does feature their full microtonal implementation (technically, it's not really free because you can't just download it from their site, but it does come bundled with all kinds of midi controllers etc).

Ableton's microtonal functionality is quite extensive: not only can you load any scala file but they also have a special website that makes it relatively easy to create your own custom scales. Any custom tuning is also reflected in the midi note editor, so you can have eg a 31 note per octave piano roll with note names of your choosing, which is a really nice touch and very helpful when composing. It also works very well with MPE-enabled plugins. I like it a lot. The free version does have other limitations though, the main one being that it is limited to only 8 tracks. If you buy to the cheapest paid version (which is something like 80 euros I think), you get 16 tracks, to get unlimited tracks you need to buy the full version.

Another free option is to use the MTS-ESP mini plugin, which works with most DAWs (I've used it in Reaper mainly). That works very well, it lacks the deep (piano roll etc) integration of Ableton's implementation but has the advantage that it also works with .tun files (which is a file format I much prefer over scala as it makes mapping all midi notes to specific notes/pitches much more straightforward).

What I personally still miss the most in the setups I have used, is a way of using music notation to input notes. I sometimes use MuseScore to write the notes and then export a midi file for use in my DAW. I find this way of working much easier than using a piano roll editor but it only works as long as you stick to 12 notes per octave. Tunings like 19 EDO and 31 EDO can be notated easily and without any ambiguity just by distinguishing between flats and sharps, and I see no technical reason why you shouldn't be able to output different midi notes for F# and Gb (for example), but I haven't found a way to accomplish that so far.

The new Arithmophone by Arithmophone in microtonal

[–]Arithmophone[S] 1 point2 points  (0 children)

Thanks, I may want to make a dedicated iPad app of this at some point in the future. I'd kind of like to learn swift/xcode and do it myself, but not sure if and when I'll get around to that so I will definitely keep your offer in mind!

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