Talk:Small comma/WikispacesArchive

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ARCHIVED WIKISPACES DISCUSSION BELOW

All discussion below is archived from the Wikispaces export in its original unaltered form.
Please do not add any new discussion to this archive page.
All new discussion should go on Talk:Small comma.



No! :(

I wanted the commas and the Unnoticeable ones back together. I don't like the way it's done now.

- PiotrGrochowski May 24, 2017, 09:21:21 AM UTC-0700

"Commas" ?

What's with all these large "commas? I think they should be moved somewhere else.

- genewardsmith January 29, 2015, 12:43:39 AM UTC-0800

What do you think is a *large comma*? Greater than 50 cent?

- xenwolf January 29, 2015, 03:41:53 AM UTC-0800

As good a definition as any.

- genewardsmith January 29, 2015, 04:19:52 PM UTC-0800

George Secor and Dave Keenan used some comma definitions depending on size in a certain introduction article for Sagittal notation*. For example, intervals larger than half an apotome (~56.8 cents) were called large dieses. Not sure how large a large diesis can be, though...

- Gedankenwelt January 29, 2015, 05:58:43 PM UTC-0800

So, maybe the biggest commas should not exceed the half tone (about 100ct), or, as to be not too western, 120ct (the half of a 5th octave)?

- xenwolf January 30, 2015, 12:46:27 AM UTC-0800

Well, there are several options. For example:

  • Since the article is called "Comma", we could borrow their definition of a comma (between ~11.7 and ~33.4 cents), and exclude everything that is larger (small, "normal" and large diesis), while optionally including or not including everything that is smaller (kleisma, schisma, schismina).
  • We could exclude everything that is larger than a "normal" diesis (> ~56.8 cents), since iirc this the definition with the largest cents value they gave.
  • We could define an upper bound for large dieses, and exclude everything above. It probably wouldn't hurt to ask them about their opinion.
  • We could simply use a more or less arbitrary cents value (like 120 or 133.33 cents), and exclude everything above.

- Gedankenwelt January 30, 2015, 05:49:12 AM UTC-0800

I was just thinking a little bit about extraterrestrial music. Isn't it reasonable to assume universal hearing range limitations for physical reasons? Putting all animals together (humans included) there is a range of slightly more than 13 octaves. After this digression, I think we should not be too restrictive with commas...

...on the other hand, commas as big as fourths seem absurd to me (to be honest)

- xenwolf January 30, 2015, 08:08:32 AM UTC-0800

Would people be OK with a cutoff of 100 cents?

- genewardsmith January 30, 2015, 08:52:10 AM UTC-0800

@xenwolf: Those large "commas" may seem absurd when looking at their size in just intonation. But on the other hand, they can become very small in certain temperaments, and tempering them out may lead to useful results, so I think it's not completely far-fetched to call them commas.

Let's take the 49-comma |78 -49> (~404 cents), for example: It may be a large interval in just intonation, but it gets fairly small in a typical superpyth tuning. And despite its large size, tempering it out means the fifths become only ~8 cents sharp (leading to 49-tet), so the "damage" to important JI intervals is much smaller than one might expect. I think tempering out the 49-comma is musically much more meaningful than tempering out 9/8, even though the latter is only half as small.

- Gedankenwelt January 30, 2015, 09:17:43 AM UTC-0800

I think any reasonable cutoff will work for now. If we'll realize later that another cutoff would be better, we can still change the list.

But where would we put the large "commas"? We could create a new article called "Large Commas", where only "commas" are allowed that are larger than 100 cents, but there should be further restrictions. For example, we may only allow commas which, if tempered out, define an equal temperament (patent val assumed) if a suitable prime limit is given, or something like that.

I also discovered an article where some methods to define the quality of a comma are specified:

http://xenharmonic.wikispaces.com/ABC%2C+High+Quality+Commas%2C+and+Epimericity

Would a generous restriction of the interval's epimericity lead to useful results?

- Gedankenwelt February 02, 2015, 06:26:10 AM UTC-0800

The boundary between our large dieses and our small semitones is at half a pythagorean apotome plus half a pythagorean comma, approximately 68.6 cents. All our boundaries are at the square-roots of 3-prime-limit ratios as follows. These boundaries allow commas to be named systematically using only their prime factors greater than 3.

0 cents

schismina

[-84 54>/2 ~= 1.8075 cents (half pythagorean schisma = half Mercator's comma)

schisma

[317 -200>/2 ~= 4.4999 cents

kleisma

[-19 12>/2 ~= 11.7300 cents (half a pythagorean comma)

comma

[27 -17>/2 ~= 33.3825 cents (half a pythagorean large-diesis = half a pythagrean limma minus half a pythagorean comma)

small-diesis

[8 -5>/2 ~= 45.1125 cents (half a pythagorean limma = half a pythagorean apotome minus half a pythagorean comma)

(medium-)diesis

[-11 7>/2 ~= 56.8425 cents (half a pythagorean apotome)

large-diesis

[-30 19>/2 ~= 68.5725 cents (half a pythagorean apotome plus half a pythagorean comma)

small-semitone

[-49 31>/2 ~= 80.3025 cents

limma

[-3 -2>/2 ~= 101.9550 cents

large-semitone

[62 -39>/2 ~= 111.8775 cents

apotome

[-106 67>/2 ~= 115.4925 cents

schisma-plus-apotome

[317 -200>/2 + [-11 7>

[295 -186>/2 ~

118.1849 cents

kleisma-plus-apotome

[-19 12>/2 + [-11 7>

[-41 26>/2 ~

125.4150 cents

etc up to double-apotome (with limma-plus-apotome also called whole-tone).

- d.keenan November 02, 2016, 06:12:37 PM UTC-0700

Go comma

I added this comma and I asked myself for its name, but suddenly the Japanese board game Go came to my mind, and its 19x19 fields that are so surprisingly close to 360... there was no reason to hesitate... ;)

- xenwolf May 19, 2013, 03:44:36 PM UTC-0700

You might as well throw in the "Boostma" of 106/105: Two months of unlimited data plus premium voicemail minus a $60 and $45 card on Boost Mobile. (Now, SoftBank, if you could please lower your premimum voicemail to $2.49 so we can pay for it easier...)

- bootmii December 03, 2016, 08:08:51 PM UTC-0800

You might as well throw in the "Boostma" of 106/105: Two months of unlimited data plus premium voicemail minus a $60 and $45 card on Boost Mobile. (Now, SoftBank, if you could please lower your premimum voicemail to $2.49 so we can pay for it easier...)

- bootmii December 03, 2016, 08:08:52 PM UTC-0800

Precision of cent values

Should we better use a unified amount of decimals, such as 4 or 5. In case of commas 4 seems a pragmatic decision for me. (Please don't ask for the precision overkill of the freqency ratios ;-) )

- xenwolf June 01, 2010, 05:41:30 AM UTC-0700

Pythagorean Integer Cents comma is funny. But it's actually 8.9998269225164511026534525240378976445421538045454906193629101364253293539449946526860196588218981646410059857998... cents

- PiotrGrochowski August 13, 2016, 09:07:54 AM UTC-0700

Pythagorean Integer Cents comma is funny. But it's actually 8.9998269225164511026534525240378976445421538045454906193629101364253293539449946526860196588218981646410059857998... cents

- PiotrGrochowski August 13, 2016, 09:07:54 AM UTC-0700

Pythagorean Integer Cents comma is funny. But it's actually 8.9998269225164511026534525240378976445421538045454906193629101364253293539449946526860196588218981646410059857998... cents

- PiotrGrochowski August 13, 2016, 09:07:55 AM UTC-0700

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