Dear Mike and Andrew,

Thank you for your speedy responses, though I think I am not explaining myself very well. I don't want to use mtof or ftom as these objects even out my ratios. What I'm looking to do is create a scale (say 12 notes for example) out of these ratio's with the possibility of filling in the consonant gaps whilst preserving the original frequencies and ratio's. The 1st number in each group is the strongest partial so: 912Hz, 1081Hz, 1211Hz etc. If I'm saying that these frequencies are 'good' to my ear, is there a way of creating equally 'good' sounding notes to fill in the gaps in, say for example, a 12 note scale based on these notes scaling from the lowest to the highest without doing the whole thing 'by ear'?

Cheers for weighing in,

Jbz

On Mon, Jul 20, 2009 at 11:16 PM, Andrew Faraday jbturgid@hotmail.comwrote:

Hey Jbz I'm not sure if this is what you want, but if you convert a midi note to frequency [mtof] then multiply by integers, you get the natural partials.

So if you multiply the outlet of [mtof] by 2 3 4 5 and 6. then you can change the multiplication figure, etc. I think that's the effect you're after.

God bless

Andrew

---

Date: Mon, 20 Jul 2009 22:24:05 +0100 From: jbeezez@googlemail.com To: pd-list@iem.at Subject: [PD] making scales from frequency values

Dear all,

I have five chimes. I've worked out the frequencies (using Audacity) of the 5 strongest partials of each chime. I now want to be able to work out how to change the octaves of the various partials? My original intention was to find the nearest midinote and just use those but after listening to the results I would much prefer to keep the original ratio's whilst being able to alter the 'inversions'.

Here's the list that I have already: BT1 912Hz 2434Hz 4575Hz 7175Hz 11584Hz

BT2 1081Hz 2861Hz 5339Hz 8325Hz 15209Hz

BT3 1211Hz 3196Hz 5935Hz 9199Hz 15206Hz

BT4 1347Hz 3553Hz 6569Hz 10128Hz 18139Hz

BT5 1812Hz 4699Hz 8525Hz 13264Hz 15469Hz

Is there one piece of mathematrical wizardy that can sort this in Pd?

Cheers,

Jbz

---

Windows Live Messenger: Happy 10-Year Anniversary—get free winks and emoticons. Get Them Now http://clk.atdmt.com/UKM/go/157562755/direct/01/

I'll be honest, this sounds a bit advanced. It's logarithmic and thus beyond me. However... Perhaps try to find a list of just temperament or world music scales and their frequencies. See if any match up to the scale you're trying to achieve.

Andrew

Date: Tue, 21 Jul 2009 00:52:24 +0200 From: derek@umatic.nl To: jbeezez@googlemail.com CC: pd-list@iem.at Subject: Re: [PD] making scales from frequency values

Still not entirely sure I know what you're after, so at the risk of repeating myself, use the (just intoned) intervals here:

1, 1:1-unison; 2, 135:128-major_chroma; 3, 9:8-major_second; 4, 6:5-minor_third; 5, 5:4-major_third; 6, 4:3-perfect_fourth; 7, 45:32-diatonic_fourth; 8, 3:2-perfect_fifth; 9, 8:5-minor_sixth; 10, 27:16-pyth_major_sixth; 11, 9:5-minor_seventh; 12, 15:8-major_seventh; 13, 2:1-octave;

I.e. major third = 6:5, and 6 divided by 5 is 1.2, so to transpose up a major third, multiply original frequency by 1.2.

Or, 5 divided by 6 is 0.83333333, so multiply by that to transpose down a major third. Or cook up something with [expr] that does the job more precisely, like [expr f$1 * (5/6)] etc etc...

All of these should "sound good" across the whole musical spectrum so long as you don't plan on changing key ;-)

D.

J bz wrote:

...

If I'm saying that these frequencies are 'good' to my ear, is there a way of creating equally 'good' sounding notes to fill in the gaps in, say for example, a 12 note scale based on these notes scaling from the lowest to the highest without doing the whole thing 'by ear'?

-- ::: derek holzer ::: http://blog.myspace.com/macumbista ::: http://www.vimeo.com/macumbista ::: ---Oblique Strategy # 126: "Only one element of each kind"

---

Pd-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list

Share your memories online with anyone you want. http://clk.atdmt.com/UKM/go/134665338/direct/01/

Ha ha, yes it's late. Of course I meant "minor third" in my example. Don't stand me against the wall for it.

D.

Derek Holzer wrote:

...

...

4, 6:5-minor_third; 5, 5:4-major_third;

...

...

I.e. major third = 6:5, and 6 divided by 5 is 1.2, so to transpose

up a

...

major third, multiply original frequency by 1.2.

Or, 5 divided by 6 is 0.83333333, so multiply by that to transpose

down

...

a major third. Or cook up something with [expr] that does the job more precisely, like [expr f$1 * (5/6)] etc etc...

Just FYI, looking at BT2,BT3 and BT4 I see that the ratios of the first partials is pretty close to a major second. Also, the ratio of the first and second partials is just about 2.64 for each of the tones you have given, which works out to something like 1 octave + a 4th (between the major and diatonic).

The attached patch lets you set the first partial frequency (either specifying the exact frequency or using the slider to select a MIDI note), then sets the remaining partials as a ratio of the first partial. I calculated the ratios using the ratios from BT2. This should give you an idea of how to maintain the spacing of the partials. You can then use a chart like the one Derek included to figure out which frequencies to use for the first partials, or you could play around and find them by hand.

Does that help at all?

andy

On Mon, Jul 20, 2009 at 4:20 PM, Dudley Brooksdbrooks@runforyourlife.org wrote:

If he's trying to make a scale which sounds "good" with notes which have non-harmonic partials (I don't have the original post to see whether the listed frequencies are, indeed, non-harmonic), then he might be interested in this:

http://ebook30.com/magazine/music/89538/tuning-timbre-spectrum-scale.html

There's another site on which you can enter the partial frequencies and it will generate a "consonant" scale for that timbre.  Unfortunately, I have lost the URL, and haven't yet successfully figured out what to search on to find it!

Surely someone on this list knows the site (and theory) I'm referring to.

-- Dudley

Derek Holzer wrote:

...

Hi Andrew,

it's really not so complicated, it's just simple math. If the root and partial frequencies of his chimes don't fit any note in an existing scale, then trying to squeeze them into one won't "sound good". It's also a lot of list-searching and ear-guessing to see what the "closest fit" might be. Using simple ratios like these will preserve the intervals of the notes no matter what the original frequencies might be.

best, D.

Andrew Faraday wrote:

...

I'll be honest, this sounds a bit advanced. It's logarithmic and thus beyond me.

However...

Perhaps try to find a list of just temperament or world music scales and their frequencies. See if any match up to the scale you're trying to achieve.

Andrew

> Date: Tue, 21 Jul 2009 00:52:24 +0200  > From: derek@umatic.nl  > To: jbeezez@googlemail.com  > CC: pd-list@iem.at  > Subject: Re: [PD] making scales from frequency values  >  > Still not entirely sure I know what you're after, so at the risk of  > repeating myself, use the (just intoned) intervals here:  >  > 1, 1:1-unison;  > 2, 135:128-major_chroma;  > 3, 9:8-major_second;  > 4, 6:5-minor_third;  > 5, 5:4-major_third;  > 6, 4:3-perfect_fourth;  > 7, 45:32-diatonic_fourth;  > 8, 3:2-perfect_fifth;  > 9, 8:5-minor_sixth;  > 10, 27:16-pyth_major_sixth;  > 11, 9:5-minor_seventh;  > 12, 15:8-major_seventh;  > 13, 2:1-octave;  >  > I.e. major third = 6:5, and 6 divided by 5 is 1.2, so to transpose up a  > major third, multiply original frequency by 1.2.  >  > Or, 5 divided by 6 is 0.83333333, so multiply by that to transpose down  > a major third. Or cook up something with [expr] that does the job more  > precisely, like [expr f$1 * (5/6)] etc etc...  >  > All of these should "sound good" across the whole musical spectrum so  > long as you don't plan on changing key ;-)  >  > D.  >  > J bz wrote:  >  > > If I'm saying that these frequencies are  > > 'good' to my ear, is there a way of creating equally 'good' sounding  > > notes to fill in the gaps in, say for example, a 12 note scale based on  > > these notes scaling from the lowest to the highest without doing the  > > whole thing 'by ear'?  >  > --  > ::: derek holzer ::: http://blog.myspace.com/macumbista :::  > http://www.vimeo.com/macumbista :::  > ---Oblique Strategy # 126:  > "Only one element of each kind"  >  > _______________________________________________  > Pd-list@iem.at mailing list  > UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list

---

Share your memories online with anyone you want. Learn more. http://clk.atdmt.com/UKM/go/134665338/direct/01/

---

Pd-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list

There seems to be some disagreement in whether the original poster wants his partials quantized to notes within an existing scale (I assume he does not) or whether he wants to preserve the exact ratios of partials to fundamental (which I assume he does). Does [tunetof] do both?

D.

Frank Barknecht wrote:

Hallo, Derek Holzer hat gesagt: // Derek Holzer wrote:

...

Still not entirely sure I know what you're after, so at the risk of
repeating myself, use the (just intoned) intervals here:

1, 1:1-unison; 2, 135:128-major_chroma; 3, 9:8-major_second; 4, 6:5-minor_third; 5, 5:4-major_third; 6, 4:3-perfect_fourth; 7, 45:32-diatonic_fourth; 8, 3:2-perfect_fifth; 9, 8:5-minor_sixth; 10, 27:16-pyth_major_sixth; 11, 9:5-minor_seventh; 12, 15:8-major_seventh; 13, 2:1-octave;

I.e. major third = 6:5, and 6 divided by 5 is 1.2, so to transpose up a
major third, multiply original frequency by 1.2.

Or, 5 divided by 6 is 0.83333333, so multiply by that to transpose down
a major third. Or cook up something with [expr] that does the job more
precisely, like [expr f$1 * (5/6)] etc etc...

Or use the [tunetof] abstraction that is a just intonation version of [mtof] and can load (after conversion) any of the thousands scale descriptions written with Scala: http://www.huygens-fokker.org/scala/

tunetof is in the svn in /abstractions/footils/tunetof

Ciao

Hey all,

First off can I say a very big thank you for everyone who's contributed so far. Some really excellent input which has helped to clarify my thinking no end.

Let's clear a few things up first:

It is a ratio problem I believe. The initial problem stems from trying to shoehorn the original ratios/partials from the analysis of my 5 chimes, into equal temperament. There are a couple of reasons for this; I've been playing around on the piano after assigning each partial to its nearest midi/equal temperament note, and was liking the results that ensued whilst listening to them on the piano. Obviously the tones generated on the piano are much richer than individual sines. The original wind chime has been sat over my desk for the last 18 months, so I'm also very attuned to the original sounds. I would also like to have the various partials to be as modular as possible with the idea that I can 'mix'n'match' the various frequencies of the chimes to create new sonorities.

When I listen to the results of using equal temperament within my patch my ears don't like the results in comparison to the original frequencies, which has led to the current predicament. As I previously stated my maths is rubbish (I'm more of a musician/composer background than computing), so when faced with the logarithmic aspect of frequency and pitch, my mind went into meltdown. But it is much clearer now (I believe).

Perhaps I should state what it is that I wish to do:

I started with the midinote idea as a hopefully simple way to be able to introduce some controlled randomness into the frequencies of the chimes whilst preserving the ratios. What I want to do is be able to assign any ratio from my analysis into any of the 5 chimes - so say have a chime consisting of the 1st partial from chime1, 2nd partial from chime2 etc.... and then any possible combination therein.

So my thinking has been to have some sort of central control which would then send the necessary value to the 5 'osc~' that make up each chime. I'm trying to conceptualise/clarify the simplest method.

I think what will make things clearer is if I forward the patch as it currently stands....

Gonna do that now

Big props peeps,

Jbz

The ratios are maintained because you're multiplying (I'm not quite sure what you mean by "even out"). But yes, you could also convert to MIDI and then use addition, and then convert back to set the oscillator. Six of one, half-a-dozen of the other.

andy

On Mon, Jul 20, 2009 at 7:06 PM, Mike Moser-Boothmmoserbooth@gmail.com wrote:

How do these objects even out your ratios (or, I guess, what do you mean by that)? Finding the difference between two frequencies after converting them to a MIDI value allows you to work linearly instead of logarithmically, which is just easier--well, for me anyway. For example, after converting 912Hz and 1081Hz to MIDI and getting the difference, you come up with 2.9431. Now you can just think of them as 2.9431 half-steps apart, and that one number will work starting from any pitch. If you stick to the frequency realm, you'll have to consider them a ratio of 912:1081, which is fine, but a little ugly and not as easy.

As far as filling in the gaps, I don't know if this will help at all or not, but it might be something to think about. When you look at how the major scale is constructed, it can be seen as taking advantage of the first few harmonics in the harmonic series. I'll use the C major scale to (try to) illustrate. Going up from C in the harmonic series, you get an octave, a fifth (G), another octave, a major third (E), and another fifth [1]. Those last three notes are a C major triad (C-E-G). Now, stepping back a bit, the first note other than C in the series is G, the fifth, or dominant, in the scale. If you go the other way, down a fifth, you get F, the subdominant. Now, taking the intervals from the C major chord and applying them to G and F, you get G-B-D and F-A-C, respectively. The notes in those chords are what is used to fill in the gaps, and now you have all of the notes of a C major scale: C-D-E-F-G-A-B.

I mention all of that because you're already working with partials. So perhaps working with an interval or ratio between two of your partials and applying that to another of your partials to generate new frequencies might get you somewhere. Or it might suck, who the fuck knows :-). Either way, this sounds like an interesting project, and I'd be interested in seeing where you go with all of this.

Best of luck, .mmb

[1] http://en.wikipedia.org/wiki/Harmonic_series_(music)

J bz wrote:

Dear Mike and Andrew,

Thank you for your speedy responses, though I think I am not explaining myself very well.  I don't want to use mtof or ftom as these objects even out my ratios.  What I'm looking to do is create a scale (say 12 notes for example) out of these ratio's with the possibility of filling in the consonant gaps whilst preserving the original frequencies and ratio's.  The 1st number in each group is the strongest partial so: 912Hz, 1081Hz, 1211Hz etc.  If I'm saying that these frequencies are 'good' to my ear, is there a way of creating equally 'good' sounding notes to fill in the gaps in, say for example, a 12 note scale based on these notes scaling from the lowest to the highest without doing the whole thing 'by ear'?

Cheers for weighing in,

Jbz

On Mon, Jul 20, 2009 at 11:16 PM, Andrew Faraday jbturgid@hotmail.com wrote:

...

Hey Jbz I'm not sure if this is what you want, but if you convert a midi note to frequency [mtof] then multiply by integers, you get the natural partials. So if you multiply the outlet of [mtof] by 2 3 4 5 and 6. then you can change the multiplication figure, etc. I think that's the effect you're after. God bless Andrew

---

Date: Mon, 20 Jul 2009 22:24:05 +0100 From: jbeezez@googlemail.com To: pd-list@iem.at Subject: [PD] making scales from frequency values

Dear all,

I have five chimes.  I've worked out the frequencies (using Audacity) of the 5 strongest partials of each chime.  I now want to be able to work out how to change the octaves of the various partials?  My original intention was to find the nearest midinote and just use those but after listening to the results I would much prefer to keep the original ratio's whilst being able to alter the 'inversions'.

Here's the list that I have already: BT1     912Hz   2434Hz   4575Hz   7175Hz 11584Hz

BT2   1081Hz   2861Hz   5339Hz   8325Hz 15209Hz

BT3   1211Hz   3196Hz   5935Hz   9199Hz 15206Hz

BT4   1347Hz   3553Hz   6569Hz 10128Hz 18139Hz

BT5   1812Hz   4699Hz   8525Hz 13264Hz 15469Hz

Is there one piece of mathematrical wizardy that can sort this in Pd?

Cheers,

Jbz

---

Windows Live Messenger: Happy 10-Year Anniversary—get free winks and emoticons. Get Them Now

---

---

Pd-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list

---

Pd-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list

On Tue, 21 Jul 2009, Lorenzo wrote:

It might be useful to think in terms ratios instead of absolute frequency values if you want to generalise your model so instead of 912, 2434, 4575 etc. 1, 2.66..., 5.01 and thus expressing all the frequencies you found experimentally as ratios. This can help when dealing with scales and 'musical' (esp. tonal) intervals because our perception of pitch is not linear (so for example the interval between 110 Hz and 220 Hz is perceived as an octave 'difference', and so is the one between 220 and 440, yet their mathematical difference is respectively 110 and 220).

Maybe you mean: as a product of ratios. This is sort of a way to introduce logararithms without introducing logarithms. I mean, before starting to do math on MIDI notes (or any other log system), conceptually, you'd multiply ratios together, but eventually, whenever multiplications become too cumbersome, you replace them by additions by using logs. Most of the theory of logarithms revolves around "multiplications are annoying, so let's use a trick to turn them into additions".

_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801, Montréal, Québec