Forums › Forums › SQ Forums › SQ general discussions › dB to Linear Taper Sum
Tagged: midi taper sum maths
This topic contains 4 replies, has 2 voices, and was last updated by SignalAudio 3 weeks, 3 days ago.

AuthorPosts

2021/03/29 at 11:07 am #100224
Hi there,
I use the TCP MIDI protocol a lot for automation from third party devices, and often need to fade up and down different sources. This ends up being quite a clunky thing to code into the controlling device as differences in fade duration require different arrays of 16bit preset values (per the linear taper in the MIDI protocol documentation).
What would help greatly is knowing the mathematical relationship between the decibel value and the 16bit linear taper value. This would mean I could program my devices to calculate the target value on the run. I’ve tried to suss it out and my wife – a statistician – couldn’t even get a particularly accurate coefficient with her clever software.
Would A&H be happy to furnish us with this? It would apply more broadly than SQ of course.
Many thanks!
2021/03/29 at 12:23 pm #100226The linear taper value is a decimal integer value between 0 and 16,383 and divided into two hexadecimal values that are both part of the value in binary mode: VC and VF.
VF is the last 7 bits of the value and VC is what remains after removing the last 7 bits.
Example: if you have a value of 15.196 (0 dB) the binary (max 14 bits) representation is 11101101011100 and hexadecima values are
VC = 1110110 = 0x76
VF = 1011100 = 0x5COther example: value 8,056 (about 60 dB) is 1111101111000 so
VC = 111110 = 0x3E
VF = 1111000 = 0x78I’ve developed a formula that returns decimal values from dB level:
decimal = integer_part(15196 + (db_level * 119))
I use this logical into my Companion module for SQ. I hope it will be useful to you.
2021/03/29 at 12:57 pm #100227Hi Max,
This is very cool. I just sussed the 14bit structure as I got the notification of your post – it was fishy that the LSB never rose above 127. I like your formula, but it does have a little – almost insignificant – error against A&H’s own table, so it’s not the sum they use, seemingly.
I recreated their hex table in the B column of a spreadsheet and wrote this function to strip the 8th bit of the LSB and shift the MSB down: =BITOR(BITRSHIFT(HEX2DEC(LEFT($B2,2))*256,1),HEX2DEC(RIGHT($B2,2)))
Your sum, working the other way from decibels (the A column in the same spreadsheet) is out by 1 at 2dB and 10 at 35dB. I wondered if it was a rounding error (integers always rounding down to the whole number), but it appears not to be, or not with your sum in this case.
Definitely not a criticism, your sum is very, very close!
Cheers..
2021/03/29 at 1:45 pm #100230I know that my formula has a bit error, only for average I using. I arrived to write “db_level * 119” because the average distance from one dB to another is “119” (0111), sometimes 118 and sometimes 120.
I think A&H’s calculations are also not accurate and in some cases what you send is not always interpreted correctly by SQ. Ad example, I send pan level to SQ for centering (3F & 7F like indicated in table of the manual) and after 200 ms I ask to it for that value: it reply with “3E & 22” (difference of 0xDD) that it is about “Left 3%”.
If I will find a way to improve the formula, I’ll share it with you. Hope you will do the same! (or A&H technicians unravel the mystery)
2021/03/29 at 9:34 pm #100241I will gladly do the same! 118.725 is almost perfect if you use conventional rounding to zero decimal places, and within +1 with integer rounding, FWIW.
Cheers.

AuthorPosts
You must be logged in to reply to this topic.