# Esoteric constant in between 16:9 and 16:10

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I need a constant in between 16:9 (0.5625) and 16:10 (0.625).  It has to be derived from some esoteric knowledge/math and not just pulled out of thin air.

THIS is the Goldie Locks and 3 Bear challenge!  Can anyone come up with such a constant?!?

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Mention of Goldielocks made me think of the golden ratio, but that's too big about 1.618033 or (1 + √5)/2. So if we take the reciprocal

2/(1+√5) = 0.618033...

Which is within your range. Tho it's got more than 3 decimal places, is that a problem?

Interestingly, 1/GR = 1 - GR which I didn't know before.

The GR has a long history, going back to the ancient world, there's a bit of information here:

Edited by Campion
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2 hours ago, Campion said:

Mention of Goldielocks made me think of the golden ratio, but that's too big about 1.618033 or (1 + √5)/2. So if we take the reciprocal

2/(1+√5) = 0.618033...

Which is within your range. Tho it's got more than 3 decimal places, is that a problem?

Interestingly, 1/GR = 1 - GR which I didn't know before.

The GR has a long history, going back to the ancient world, there's a bit of information here:

That's not it.  16:10 IS the golden ratio!

BTW, so if anyone don't get the OP, Papa bear is the Golden Ratio 16:10, while Mama bear is the ubiquitous 16:9 ratio of most modern TVs.

Obviously, Baby bear will sit in between Papa bear and Mama bear.

So, plz let's hear more suggestions about Baby bear!

Edited by sphere555
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2 hours ago, sphere555 said:

That's not it.  16:10 IS the golden ratio!

BTW, so if anyone don't get the OP, Papa bear is the Golden Ratio 16:10, while Mama bear is the ubiquitous 16:9 ratio of most modern TVs.

Obviously, Baby bear will sit in between Papa bear and Mama bear.

So, plz let's hear more suggestions about Baby bear!

Ok then   . But does the Goldilocks story itself have any esoteric meanings? It might help think of a number. I've long suspected that fairy stories contain hidden meanings but haven't found a good source.

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16:10 and 16:9 might seem so close that it's impractical to fit anything in between!  Really?  0.5625 and 0.625 are so far apart it's very feasible to obtain an in-between value!

Edited by sphere555
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What exactly do you mean by esoteric? I could suggest 19/32, but obviously that's not what you're looking for.

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I can give you some ratios from the 43-tone per octave tuning that Harry Partch used.

He decided Just Intonation was the way to go and the ear likes low ratios like 3:2 = the Perfect Fifth - not the fake 'Perfect Fifth' you get in Equal Temperament.

Is that esoteric enough for you? His music certainly ought to be! I think it's good if that helps.

tone 30 = 8/5 = 16/10 = 0.625

tone 31 = 18/11 = 0.6111

tone 32 = 5/3 = 0.6000

tone 33 = 27/16 = 0.5926

tone 34 = 12/7 = 0.5833

tone 35 = 7/4 = 0.5714

tone 36 = 16/9 = 0.5625

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• 4 weeks later...
On 2/6/2024 at 6:08 PM, gregory-peccary said:

tone 30 = 8/5 = 16/10 = 0.625

.

.

tone 33 = 27/16 = 0.5926

.

tone 36 = 16/9 = 0.5625

I ended up going with this value.  I also want to add that if you add 7-11 (which in itself is a very esoteric numbers pair) to 16:9, you get 16+11:9+7 , which is 27:16 (or 0.5926)!

Edited by sphere555

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