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 Forum index » DIY Hardware and Software » Developers' Corner
Tolerance Tuning Tables
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Tony Deff



Joined: May 25, 2008
Posts: 42
Location: Suffolk, UK

PostPosted: Mon Apr 27, 2009 2:51 pm    Post subject:  Tolerance Tuning Tables
Subject description: Frequency look-up tables with ± 2cent tolerances
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In the realm of Electronic Music, we have occasion to ensure that our note generators are not only in-tune with the outside world, but also with each other (in-scale). This is especially true of so-called "free-phase" instruments, which have multiple banks of oscillators.

A conventional frequency look-up table (FLUT) gives the tuner little notion of the limits of acceptable accuracy: is a 0·5 Hz. error at 440 Hz. acceptable? The table here may not give the exact tolerance that you require, but it does allow you to judge the accuracy.

The decimal resolution required depends both on the frequency and what degree of key-colour change (variance from a precise scale, so that a change of key produces a slight change of interval accuracy) is acceptable. Often you have little control over how your hardware (oscillators and frequency meter) reacts. A tolerance table gives a much better indication of the degree of tuning errors.

For the lowest notes, the decimal resolution of frequency meters is usually inadequate. Some meters provide an inverse indication as a time period, measured in milli­seconds or microseconds. Conversely, for the higher notes the decimal resolution of time periods is inadequate, and display of frequency is to be preferred: this table provides that choice.

The table is produced using “spreadsheet technology”, avoiding type­setting errors found slavishly duplicated in some older publications.
(It also allows tables to be produced for other absolute pitches, for example an older standard where C = 256 Hz. If you need such a table, just ask). The maths involved has already been published in the article Harmonic Logarithms, so you can also produce your own tables.

Octave Designations

There are many confusing, contradictory and arbitrary notations for the designation of octave pitches (organ "footages"). The first system to be widely-accepted was proposed by Baron Herman Ludwig Ferdinand Helmholz (1821-1894) in a publication of 1863.

Since then , there have been different national and arbitrary systems in use. The MIDI standard does not specify octave notation, so C5 or C3 might be used in documen­tation to represent middle C (note #60), and some books may mix systems without remark.

The system incorporated here is that proposed by the Acoustical Society of America in London in July 1939, viz. Scientific Pitch Notation, where C0 marks the nether-region below which sound is perceived more by the intestines than the ear. A4 refers to A=440·0 Hz. (above middle C4).
(If an international meeting in 1939 can meet to agree the pitch of A = 440Hz, rather than being concerned with trivialities such as preventing catastrophic global war, then it must be extremely important!)

Scientific pitch notation is an unambiguous specification of a note as a fixed frequency. Conventional pitch notation may specify a written and an actual compass of a transposing instrument.


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Rykhaard



Joined: Sep 02, 2007
Posts: 1290
Location: Canada

PostPosted: Mon Apr 27, 2009 5:07 pm    Post subject: Reply with quote  Mark this post and the followings unread

Thank you GREATLY for posting THIS! Surprised Very Happy

I was JUST searching for note pitches to know what I need to tune my voices to, in my CMOS String Machine that I'm building, from scratch. This will come in majorly handy for the equal temperament scale! Very Happy

(Now, I'd like to find the same thing for at least the Even Temperament tuning standard and other 12 note tuning systems. Shall search.)
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JovianPyx



Joined: Nov 20, 2007
Posts: 1235
Location: West Red Spot, Jupiter
Audio files: 158

PostPosted: Mon Apr 27, 2009 5:12 pm    Post subject: Reply with quote  Mark this post and the followings unread

Wow, that's very interesting technical information.

I read an article (can't cite a URL, sorry but I'm sure Google can help) that said that most humans don't perceive a badly tuned scale if the notes are all within 5 cents of "perfect". Given that, I would say that plus or minus 2 cents would be at least good enough. Even if pitches could be perfectly computed for concert pitch tuning, there will be phasing heard with intervals. A simple 5th is slightly off from a true perfect 5th, you hear a nice phasing beat sound. A bit of tuning inaccuracy will speed or slow that effect but if you're within +/- 2 cents I wouldn't hear anything I'd call "sour".

In my own synth designs, I use rather wide phase accumulators and phase increment registers (usually 32 bits or more). The sample rates are usually 200KHz to 1.0MHz with one or two designs as low as 65KHz. It is my understanding that wider phase accumulators and phase increment arithmetic allows for better tuning accuracy. Such wider arithmetic is supported by higher sample rates. I compute my tuning tables with the usual K*2^(N/12) formula.

The bottom line for me - my ears. I tune everything by ear and get the tuning effects (phasing) I want by using my ears.

I hope that helps.

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Rykhaard



Joined: Sep 02, 2007
Posts: 1290
Location: Canada

PostPosted: Mon Apr 27, 2009 5:30 pm    Post subject: Reply with quote  Mark this post and the followings unread

When I was setting up the tuning for pairs of CD40106 oscillators, I found that using a 100k summing node to a non-inverting 100k feedback, the closer that the 2 'oscillators' were to the exact required pitch, the greater the chances were of completely cancellation of amplitude. Sad

In working to find where they were both clearly oscillating audibly, with the 100k summing, I needed a detuning range for the 2 x C#5 (554.365hz) notes of about 551hz to 557hz ...... wassat? About 6 to 8 cents between them overall?
This gave me a chorusing effect at about 8 to 12hz / second. My goal for the oscillator pairs for each 'voice' is about 5 to 8hz / second. I'm going to try what's done for the SSM2044 chip's 2 audio inputs - a difference of 3dB that they specified for it, to avoid cancellation between 2 oscillators.
With square waves, I'm hoping it'll work. If not - I'll have to stick with the wider chorusing effect.
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Tony Deff



Joined: May 25, 2008
Posts: 42
Location: Suffolk, UK

PostPosted: Tue Apr 28, 2009 2:35 pm    Post subject: Reply with quote  Mark this post and the followings unread

Rykhaard wrote:


I was JUST searching for note pitches


Now I know where the vibes for me to complete this posting were coming from. I had been holding off, fearing the Turkey Award for the most boring post of the month.

Rykhaard wrote:
When I was setting up the tuning for pairs of CD40106 oscillators, I found that using a 100k summing node to a non-inverting 100k feedback, the closer that the 2 'oscillators' were to the exact required pitch, the greater the chances were of completely cancellation of amplitude.


Que? What is canceling what? I am not familiar with your oscillators, but with simple Schmitt trigger technology would fear for their stability and also for cross-coupling problems. Is this what might be happening?

ScottG wrote:

I read an article (can't cite a URL, sorry but I'm sure Google can help) that said that most humans don't perceive a badly tuned scale if the notes are all within 5 cents of "perfect"


Yes, I've seen that too, "JND"

http://en.wikipedia.org/wiki/Just_noticeable_difference

http://tf.nist.gov/general/glossary.htm

Also did a bit of searching various links and found this site offering conversion to/from cents:

http://www.sengpielaudio.com/calculator-centsratio.htm

and also frequency to note-name plus offset in cents:

http://www.birdsoft.demon.co.uk/music/notecalc.htm

and also changing a sample rate to effect a frequency shift measured in cents
http://www.birdsoft.demon.co.uk/music/samplert.htm

I'd also completely agree with you about phasing (beats by any other name would sound as sweet — did Shakespeare say that?). Our 12ET scale is critical in the temperament of the fifth, which is only 2 cents from a Just interval. It is temperamental and can soon lose its temper.
A 5-cent tolerance would change that to either 7 cents or 3 cents (the other way), noticeably changing the beats.

Talking of beats, I was wondering whether to unleash a proposal for a simple Choral effect, but did not know how many cents offset made an ideal chorus. My system would give a fixed nominal 4-cent offset, but translated into beats gives a different answer for each octave.
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Rykhaard



Joined: Sep 02, 2007
Posts: 1290
Location: Canada

PostPosted: Tue Apr 28, 2009 2:56 pm    Post subject: Reply with quote  Mark this post and the followings unread

Tone-Deaf wrote:
Rykhaard wrote:


I was JUST searching for note pitches


Now I know where the vibes for me to complete this posting were coming from. I had been holding off, fearing the Turkey Award for the most boring post of the month.


Nossirree! This has worked out beautifully, timing wise!

Quote:

Rykhaard wrote:
When I was setting up the tuning for pairs of CD40106 oscillators, I found that using a 100k summing node to a non-inverting 100k feedback, the closer that the 2 'oscillators' were to the exact required pitch, the greater the chances were of completely cancellation of amplitude.


Que? What is canceling what? I am not familiar with your oscillators, but with simple Schmitt trigger technology would fear for their stability and also for cross-coupling problems. Is this what might be happening?


I have to wonder if it could be cross-coupling that is causing the sound of both of them to then, cancel out? I'm unsure - if the tuning of the 2 Schmitt Trigger Inverters are within 2 to 3 hz of each other, they completely cancel out, audibly. Sad

Stability is what at least 1 person her told me I would have troubles with, about 18 months ago when I first proposed my idea of a CMOS String Machine.
In my tests over the last few days, I've proven that worry to be untrue.

Testing 6 oscillators in 1 chip, with 5% carbon resistors and polyester film capacitors, over a 36 hour period, the greatest amount of pitch drift that I experienced, was approximately 0.3%!! Smile And that was from only 1 oscillator who's initial tuning frequency I may not have written down properly.
The greatest frequency drift from initial settings for either of the other 5 oscillators was 0.21%. Well within the 0.25% 1V/octave tuning standard maximum deviation. Smile (Which I'm not worried about anyways, as the String Machine is being built for use within a Noise Machine, anyways. Wink )

Stability of the 6 oscillators set up for 2 osc's each playing the same frequency, set up as a minor chord, worked beautifully as well. A luscious full chorus that stayed in tune.

I'm now going full blast ahead to make a 2 octave 2 voice string machine, around the CD40106 (hex Schmidt Inverter).

Again - thankee for posting the tuning spreadsheet! As well as the further links! Smile
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