Just Intonation post (with tuning list shout-out!)

I've just spent the better part of today writing a post on just intonation, which of course would be elementary review for pretty much everyone here, but if anyone feels like reading through it to see whether I botched anything terribly, I'd appreciate any polite feedback. I even threw in a shout-out to this list! ;-)

http://miskatonal.blogspot.com/2011/06/just-intonation.html

It looks pretty decent to me. I didn't notice any information that was noticeably wrong. I would present a couple of things differently, if this little essay is meant to introduce the concept to initiates:

In your two tables, I think that you should present more information about what is in them beforehand. For example, your first table lists ratios and the interval names; I think it would be clearer if you say beforehand what that ratio means rather than afterwards. Specifically, I think that it's important to give an example of how thise ratios literally affect the pitch in Hertz, something like this:

"Let's say we have a pitch of 100 Hz, which is about a G. The perfect fifth, 3:2, means that 100 Hz becomes 100*3/2, or 150 Hz."

It is slightly more math, but I think that it's necessary for clarity.

Also, I don't think that it's necessary to go through all of the non-English names for the intervals, but that's just my opinion.

Andrew

--- In tuning@yahoogroups.com, "Jay Random" <cortaigne@...> wrote:
>
> I've just spent the better part of today writing a post on just intonation, which of course would be elementary review for pretty much everyone here, but if anyone feels like reading through it to see whether I botched anything terribly, I'd appreciate any polite feedback. I even threw in a shout-out to this list! ;-)
>
> http://miskatonal.blogspot.com/2011/06/just-intonation.html
>

Thanks for checking it out, Andrew! Based on your feedback, I've added this section before the first table:

"The mathematical procedure to apply these ratios is relatively straightforward: a basic pitch is chosen, and the frequency of that pitch is multiplied by the desired ratio to arrive at the second pitch. For example, standard concert tuning is known as A440, because the A above Middle C is set at 440 Hz (Hertz, a unit that measures vibrations per second). If we take this as our basic pitch and want to find the pitch at a ratio of 3:2 above it, we'd have 440*(3/2) = 660 Hz."

I agree it was necessary for clarity, so I appreciate you mentioning it. :-)

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> It looks pretty decent to me. I didn't notice any information that was noticeably wrong. I would present a couple of things differently, if this little essay is meant to introduce the concept to initiates:
>
> In your two tables, I think that you should present more information about what is in them beforehand. For example, your first table lists ratios and the interval names; I think it would be clearer if you say beforehand what that ratio means rather than afterwards. Specifically, I think that it's important to give an example of how thise ratios literally affect the pitch in Hertz, something like this:
>
> "Let's say we have a pitch of 100 Hz, which is about a G. The perfect fifth, 3:2, means that 100 Hz becomes 100*3/2, or 150 Hz."
>
> It is slightly more math, but I think that it's necessary for clarity.
>
> Also, I don't think that it's necessary to go through all of the non-English names for the intervals, but that's just my opinion.
>
> Andrew
>
> --- In tuning@yahoogroups.com, "Jay Random" <cortaigne@> wrote:
> >
> > I've just spent the better part of today writing a post on just intonation, which of course would be elementary review for pretty much everyone here, but if anyone feels like reading through it to see whether I botched anything terribly, I'd appreciate any polite feedback. I even threw in a shout-out to this list! ;-)
> >
> > http://miskatonal.blogspot.com/2011/06/just-intonation.html
> >
>

My pleasure. Just Intonation is my area of interest in this group, so I try to contribute as best as I can when it comes up.

Andrew

--- In tuning@yahoogroups.com, "Jay Random" <cortaigne@...> wrote:
>
> Thanks for checking it out, Andrew! Based on your feedback, I've added this section before the first table:
>
> "The mathematical procedure to apply these ratios is relatively straightforward: a basic pitch is chosen, and the frequency of that pitch is multiplied by the desired ratio to arrive at the second pitch. For example, standard concert tuning is known as A440, because the A above Middle C is set at 440 Hz (Hertz, a unit that measures vibrations per second). If we take this as our basic pitch and want to find the pitch at a ratio of 3:2 above it, we'd have 440*(3/2) = 660 Hz."
>
> I agree it was necessary for clarity, so I appreciate you mentioning it. :-)
>
>

> The distance between the diapente and the diatessaron was called the > tonus, ratio 9:8, what is today called a whole tone or a major second

It's a small point.. but it might be worth omitting 'major second' from this sentence.
'9:8' and 'whole tone' are clear intervals but 'major second' is a matter of spelling.

> The pure intervals have been tempered to equal widths for the sake > of conveniences like unhindered transposition and modulation. > However, the cost of this compromise is the loss of the distinctive > characters of each key and their modes

JI doesn't of necessity restore the distinctive characters of keys, unlike (for example) some of the (unequal) historic temperaments.

It could be a nice addition to explain how just modal tuning differs from modes as taught in Colleges and Universities these days - Equal Ionian tuning starting on different roots..

Steve P.

--- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:
>
> > The distance between the diapente and the diatessaron was called the
> > tonus, ratio 9:8, what is today called a whole tone or a major second
>
> It's a small point.. but it might be worth omitting 'major second'
> from this sentence.
> '9:8' and 'whole tone' are clear intervals but 'major second' is a
> matter of spelling.

True! Done; also updated the first table. A good suggestion, thanks. :-)

> > The pure intervals have been tempered to equal widths for the sake
> > of conveniences like unhindered transposition and modulation.
> > However, the cost of this compromise is the loss of the distinctive
> > characters of each key and their modes
>
> JI doesn't of necessity restore the distinctive characters of keys,
> unlike (for example) some of the (unequal) historic temperaments.
>
> It could be a nice addition to explain how just modal tuning differs
> from modes as taught in Colleges and Universities these days - Equal
> Ionian tuning starting on different roots..

Also a good suggestion, but this is a can of worms I'm not prepared to open at the moment, primarily because I'm still a little hazy on it (I took choir in junior high and that's the last "formal" music education I had). Perhaps in a future post. ;-) Could you recommend a good resource on this subject?