also...

>>> 10 9 199.61 17.209 2.6508
>>> 9 8 199.61 4.2977 0.69655
>>> 6 5 299.42 16.223 3.3061
>>> 5 4 399.22 12.911 2.9873
>>> 4 3 499.03 0.98586 0.275
>>> 3 2 698.64 3.3118 1.2812
>>> 8 5 798.45 15.237 2.863
>>> 5 3 898.26 13.897 3.557
>>> 9 5 998.06 19.535 3.557
>>> 2 1 1197.7 2.3259 2.3259
//
>! zeta12.scl
>!
>12 equal zeta tuning
> 12
>!
>99.807
>199.614
>299.422
>399.229
>499.036
>598.843
>698.650
>798.457
>898.265
>998.072
>1097.879
>1197.686
>
>...Notice the similarity...

Also...

/tuning-math/message/894

>15
>Gram tuning = 15.052, 4.14 cents flat
>Z tuning = 15.053, 4.26 cents flat

Ok, so following Paul's method I'll take the 5-limit
val < 15 24 35 ] and divide pairwise by log2(2 3 5),
then find the average 15.07115704285749, divide the
original val by it giving...

< 0.9952785945594528 1.5924457512951244 2.322316720638723 ]

...and then * 1200...

< 1194.3343134713434 1910.9349015541493 2786.7800647664676 ]

(Is ket notation appropriate here? What is this, h1194.3343134713434
or h1200 or...?)

This is not apparently the Gram or the Z tuning. To the 7-limit...

< 1195.8934635210232 1913.4295416336372
2790.4180815490545 3348.5016978588646 ]

...this is close to the Gram tuning if I understand Gene's
nomenclature there. Howabout the 17-limit...

< 1197.365908554304
1915.7854536868863
2793.8537866267093
3352.6245439520508
4150.868482988254
4470.166058602735
4869.288028120835 ]

...whoops, we blew it.

>19
>Gram tuning = 18.954, 2.93 cents sharp
>Z tuning = 18.948, 3.29 cents sharp

5-limit...

< 1202.2814046729093 1898.3390600098567 2784.2306213477896 ]

7-limit...

< 1203.8338650199978
1900.7903131894698
2787.8257926778892
3358.06288663473 ]

11-limit...

< 1201.3512212496696
1896.8703493415835
2782.076512367656
3351.137617170131
4173.114768551483 ]

31-limit...

< 1201.2099597644576 //

...no cigar.

>22
>Gram tuning = 22.025, 1.35 cents flat
>Z tuning = 22.025, 1.37 cents flat

5-limit...

< 1198.7183021467067 1907.051844324306 2778.846973158275 ]

7-limit...

< 1198.6555970781733
1906.9520862607305
2778.7016114084927
3378.0294099475796 ]

11-limit...

< 1198.6555970781733 //

...looks like we might have a winner here.

By the way, I've decided I like the square bracket for
ket notation, because it avoids confusion with abs. |n|,
Euclidean distance or norm or whatever ||n|| is.

-Carl

[I wrote...]

>/tuning-math/message/894
>
>>15
>>Gram tuning = 15.052, 4.14 cents flat
>>Z tuning = 15.053, 4.26 cents flat
>
>Ok, so following Paul's method I'll take the 5-limit
>val < 15 24 35 ] and //
>
>< 1194.3343134713434 1910.9349015541493 2786.7800647664676 ]
>
>(Is ket notation appropriate here? What is this, h1194.3343134713434
>or h1200 or...?)
>
>This is not apparently the Gram or the Z tuning. To the 7-limit...
>
>< 1195.8934635210232 1913.4295416336372
> 2790.4180815490545 3348.5016978588646 ]
>
>...this is close //
>
> Howabout the 17-limit...
>
>< 1197.365908554304
> 1915.7854536868863
> 2793.8537866267093
> 3352.6245439520508
> 4150.868482988254
> 4470.166058602735
> 4869.288028120835 ]
>
>...whoops, we blew it.

Maybe I shouldn't be using the standard val at limits in
which the ET is not consistent?

>>19
>>Gram tuning = 18.954, 2.93 cents sharp
>>Z tuning = 18.948, 3.29 cents sharp
>
>5-limit...
>
>< 1202.2814046729093 1898.3390600098567 2784.2306213477896 ]
>
>7-limit...
>
>< 1203.8338650199978
> 1900.7903131894698
> 2787.8257926778892
> 3358.06288663473 ]
>
>11-limit...
//
>...no cigar.

!

>>22
>>Gram tuning = 22.025, 1.35 cents flat
>>Z tuning = 22.025, 1.37 cents flat
>
>5-limit...
>
>< 1198.7183021467067 1907.051844324306 2778.846973158275 ]
>
>7-limit...
>
>< 1198.6555970781733
> 1906.9520862607305
> 2778.7016114084927
> 3378.0294099475796 ]
>
>11-limit...
>
>< 1198.6555970781733 //
>
>...looks like we might have a winner here.

Going to the 13-limit...

< 1200.7057937136167
1910.2137627262084
2783.454339972475
3383.8072368292833
4147.892741919766
4420.780422309225 ]

...the value seems to change sharply here too.

-Carl