Just & Equal Temperaments

[Meffy]

Obviously a sanguine.

[Kingston]

What about those four other temperaments? Someone (not I) should devise choleric, phlegmatic, sanguine, and melancholic musical temperaments.

... On second thought, it's probably been done.

I would add to the list, bad temperament. I certainly experienced it when I managed to break the high E string of the guitar yesterday and found out I had no replacement at hand.

[rp314]

stockhausen kicks ass!

Sooner or later the truth finds its way into most KVR threads.

[Meffy]

@Kingston: Of course -- the opposite of Good Humor, the legendary Fifth Bodily Humor (long thought to have been Beef Stew Sutcliffe). The fluid associated with the Good Humorous Temperament is melted ice cream.

[Dreamw]

But the bearing of the length of the second on "Hz" is totally irrelevant.

Even if you change the length of the second to something you find "less arbitrary" (though it seems mighty arbitrary of you to toss out a centuries-old convention on a whim because you don't like it), the ONLY thing that changes is the number value of the frequency measurement.

Whether you measure frequency in cycles/second or half-cycles/one-sixty-fourth-minute or gnargls/buttflecks, it's still frequency; the octave is still double whatever number you measure.

It has no musical bearing whatsoever since tuning systems (and the way the ear hears notes) is based on cents (ratio intervals) rather than absolute measures of frequency.

Thanks for the coherent response . Well of course, I realisethis, but it does matter if you are doublings of "one" of these units to base your octaves on (doublings being 2,4,8,16,32,64,128,256 etc) As all the subsequent frequencies are mathematically derived from this "one" I wanted it to be related to a natural cycle.
As for throwing out the length of the second its not arbitrary at all - its no different to going metric. It just seemed strange that days and years correspond to a cycle of nature but seconds, minutes and hours didnt. I m not suggesting changing the calender or anything, just looking at other approaches to sound.
Annnnyyyywaaay this thread has gone a little of topic and was frankly I was starting to feel a little stressed out which seems pointless. Perhaps another time/thread would be more appropriate.
All I wanted to say to the person that started the thread really is that he can do anything he wants with just intonation using max msp -he can even defeat the pythagorian comma ! Also that Im up for collaborating with anyone experimenting with musical scales and just intonation . Im sure people have got valuable knowledge I dont and it would help refine ideas and come up with new ones .

[Dreamw]

stockhausen kicks ass!

I believe he claims hes from sirius ?
I like GESANG DER JÜNGLINGE.

[Toxikator]

it does matter if you are doublings of "one" of these units to base your octaves on (doublings being 2,4,8,16,32,64,128,256 etc) As all the subsequent frequencies are mathematically derived from this "one" I wanted it to be related to a natural cycle.

But why? No one note sounds inherently better than any other; music is about placing notes in context. A single frequency is largely irrelevant. Sure, how high or low it is with relation to the maximums/minimums of our ear's frequency response is relevant, but I mean beyond that.

If you remeasure your tuning system so that A != 440Hz, you've accomplished nothing of real musical significance. Orchestras do it all the time, due to instrument error, volume control, or both. You can redefine the system of measure around anything you like but at the end of the day you're still left with a single frequency value, which is musically meaningless. Be it 440Hz, 220Hz, 122.3443Hz, 4 Shirtz, 3006 Quartz, 26 Kilofreqs or 1 Tunedeforce, it doesn't matter. It will still just be a pitch.

It's the ratios that matter, and the Hz system of measurement has precisely zero bearing on it.

[Dreamw]

it does matter if you are doublings of "one" of these units to base your octaves on (doublings being 2,4,8,16,32,64,128,256 etc) As all the subsequent frequencies are mathematically derived from this "one" I wanted it to be related to a natural cycle.

But why? No one note sounds inherently better than any other; music is about placing notes in context. A single frequency is largely irrelevant. Sure, how high or low it is with relation to the maximums/minimums of our ear's frequency response is relevant, but I mean beyond that.

If you remeasure your tuning system so that A != 440Hz, you've accomplished nothing of real musical significance. Orchestras do it all the time, due to instrument error, volume control, or both. You can redefine the system of measure around anything you like but at the end of the day you're still left with a single frequency value, which is musically meaningless. Be it 440Hz, 220Hz, 122.3443Hz, 4 Shirtz, 3006 Quartz, 26 Kilofreqs or 1 Tunedeforce, it doesn't matter. It will still just be a pitch.

It's the ratios that matter, and the Hz system of measurement has precisely zero bearing on it.

Toxilator -
Thanks for your patience. The reason why is because I have a theory that there is some kind of natural order to sound that I (and many others) have touched on by going outside the musical structures we have been culturally conditioned with . Schoenberg made that point years ago .
Id like to find these structures if they exist and then play around with them. I understand that the ratios are what matter and not the starting frequency though actually thats not strictly true - theres millions frequencies that will never be played because they do not fit anywhere in the Chromatic scale (the gap between semitones covers a lot of frequencies) unless you change the frequency for C or whatever, so changing the starting frequency would give you access to frequencies you would otherwise never hit (microtonal ?) . But this is not the reason why - the reason why is that I think its possible that if the "correct" unit is used to start with (eg a scale based on cycles per unit of time related to a naturally occuring cycle such as the atomic clock etc) and precise multiples of this "correct" unit are used for the octaves ( the ratios also being precise whole number ratios) then the music may have some rather unusual effects. Of course I may be wrong but this is what I am experimenting with to find out - theory - experiment - basic scientific method.

[apollo33]

What the heck happened to my thread?

I hope it's clear now that Dreamw is just looking for "the perfect frequency" to base a scale on, and people can stop arguing about how to measure frequency.

I just have a few comments, which I'm mostly unqualified to make, but as the OP I figure it's my right.

No one note sounds inherently better than any other;

Have you considered that some people have perfect pitch?

Dreamw:
I was trying to think of some naturally occurring frequencies for you. I came up with (1) the frequency at which light would reflect off of 2 mirrors placed some 'natural constant' distance apart, like Planck's or something (and then probably halved a million times till you could hear it ), and (2) I think molecules have some type of vibrational frequency according to their temperature, so maybe something like the frequency at which a water molecule changes from a liquid to gas.

But then I realized something: music is for your ears. So the only really logical place to look for a frequency to start on should be based on your ears. Then I would suggest just playing a sine wave through a range of frequencies and listening for one that stands out somehow. Other than that, I think you'd just be playing around with numbers for no reason.

EDIT: Another comment for Dreamw:
You said about looking for the perfect interval to base a scale on. I think if you look at the overtones for a simple plucked/hammered string (octaves, fifths, third), those are the best sounding intervals you're going to get. If you want others, again I'd say to play two sine waves, keep one constant, vary the other, and listen for nice sounding intervals. You've probably already done both of my simple sine wave suggestions, but like I said before, your ear is the only measure of how well something sounds, so unfortunately math is most likely useless.

[Dreamw]

What the heck happened to my thread?

I hope it's clear now that Dreamw is just looking for "the perfect frequency" to base a scale on, and people can stop arguing about how to measure frequency.

I just have a few comments, which I'm mostly unqualified to make, but as the OP I figure it's my right.

No one note sounds inherently better than any other;

Have you considered that some people have perfect pitch?

Dreamw:
I was trying to think of some naturally occurring frequencies for you. I came up with (1) the frequency at which light would reflect off of 2 mirrors placed some 'natural constant' distance apart, like Planck's or something (and then probably halved a million times till you could hear it ), and (2) I think molecules have some type of vibrational frequency according to their temperature, so maybe something like the frequency at which a water molecule changes from a liquid to gas.

But then I realized something: music is for your ears. So the only really logical place to look for a frequency to start on should be based on your ears. Then I would suggest just playing a sine wave through a range of frequencies and listening for one that stands out somehow. Other than that, I think you'd just be playing around with numbers for no reason.

Thanks Apollo
With that first sentence you have very succinctly summed up what I was trying to say - at least someone understands me Yes I understand what you are saying about music and you have some interesting ideas there which could be useful I shall chew them over. Of course sound can be used for other things apart from music and it might be interesting to include frequencies in music that had certain physiological/psychological effects . The ear is a good place to look hadn't thought of that, and of course theres the different way the brain reacts, certainly different frequencies/rhythms have different effects on the way we hear music, and often these frequencies fall outside the equal tempered scale. I was of wondering if there was a relationship between whole number ratios and these effects on the brain. Probably not but I wonder.

[Dreamw]

but like I said before, your ear is the only measure of how well something sounds, so unfortunately math is most likely useless.

I agree with this completely - in fact my ear is what judges whether the experiment is successful or not. Where I feel a lot of contempory composers such as Xenakis fall down sometimes.
I met a guy who said he got into just intonation . He said at first it sounded off key but after a while it just sounded "right" after that all music written in the equal tempered scale sounded out of key. This has been reported by a couple of musicians, so perhaps the fact that the ratios are precise mathematical divisions of the octave does have an effect on the perceived quality of the music . eg perfect fifth is maths and that works so there may be some relationship between maths and what sounds good ( eventually);

[Toxikator]

No one note sounds inherently better than any other;

Have you considered that some people have perfect pitch?

Barring synesthesiates (of whom there are very few in the entire world, though a good number have been musically important), perfect pitch is just a form of pitch memory. Even those who can tell an E from a Bb aren't going to prefer one to the other; they're just pitches.

Those who DO experience sound as color may do so differently, but they are extremely few and far between.

[apollo33]

Well yeah, fifths can be calculated, but they're also naturally occurring. So I guess my point is that it seems pointless to do a bunch of math (unrelated to music) to come up with a frequency or interval, and then listen to it and see if it sounds good, when you could do a sine sweep to hear all the frequencies/intervals in the first place. I'm just trying to save you a lot of time .

Since this has already gone off topic and we're talking about unique frequencies, does anyone here have perfect pitch, and do some frequencies really sound brighter or softer than others? 'Cause I was listening to this David Burge perfect pitch lecture, and he says that everyone hears F# as brighter than the other notes.. but I don't hear any difference.

[Dreamw]

Well yeah, fifths can be calculated, but they're also naturally occurring. So I guess my point is that it seems pointless to do a bunch of math (unrelated to music) to come up with a frequency or interval, and then listen to it and see if it sounds good, when you could do a sine sweep to hear all the frequencies/intervals in the first place. I'm just trying to save you a lot of time .

Since this has already gone off topic and we're talking about unique frequencies, does anyone here have perfect pitch, and do some frequencies really sound brighter or softer than others? 'Cause I was listening to this David Burge perfect pitch lecture, and he says that everyone hears F# as brighter than the other notes.. but I don't hear any difference.

Ill probably do both as the ear often judges just intonation to be wrong at first and then later adjusts to it so partly what "sounds good" could be culturally conditioned, Schoenberg made music that sounded horrible to many people at first but who later became totally addicted to it so, but I take your point especially with regard to physiological effects.
I do not have perfect pitch so cannot really answer your second question. I would have thought brightness has more to do with the waveform than note.

[apollo33]

Hmm, ok, I see your point if it takes a while to get used to the new sound. Then some kind of mathematical theory would be a shortcut, since you can't just do a sweep like I said. But then I take it every time you come up with a new theory or scale, you have to torture yourself with it for like a week before you can decide if it would be good or not?