This is whistle related - just. I am writing a whistle hole calculating program, essentially a repackaging of Daniel Bingamon’s algorithm from TWCalc, but with some extra features.
TWCalc has an in built ‘collection of notes’ (‘note’ here means a ‘named frequency’ such as A3 = 220hz). This ‘collection of notes’ could be described by as being '12 tone equal temperament where A = 440hz. (12 TET A=440). From my reading of this forum I gather that there may be many other ‘collections of notes’ based on different numbers of notes per octave, different relationships between the notes, or both.
My question is: What is the generic name for one of these ‘collections of notes’.
A supplementary question would be: Would allowing the user to define different ‘collections of notes’ be useful. It would bbe relatively easy to add to the program. Such a feature would be most useful in conjunction with user defined ‘Scale Patterns’. These are almost implemented.
I don’t know of a music theory term for such, but mathematically you got a set, if I understand you correctly. So “set of notes” or "set of note frequencies"may be an appropriate term.
But isn’t any of such sets of notes determined by the musical mode used, as well as a lowest and a highest note in the set? And if we are talking about a set of note frequencies, it is of course determined also by a base frequency, like A=440Hz.
I am using “musical mode” in a wide context, to include all kinds of modes, not just 12 tone ET modes. See this list of musical modes. Any set of note frequencies can be calculated from a given mode and a base frequency and limits for lowest and highest frequency in the set.
The ‘set of notes’ that I refer to is something like the ‘set of all notes that could be used in this musical context’. This set is potentially infinite (at least in theory) and members are probably generated by some underlying definition. From this set we tend to select a subset using a pattern (eg 2 2 1 2 2 1) and a starting point - one of the notes, (eg D) and get a set of notes used in one particular piece of music (eg D Major). The note names and selection patterns used may be different for a different ‘set of all notes that could be used in this musical context’
But 12TET A440 is not the only ‘set of all notes that could be used in this musical context’. There are (perhaps many) just tunings, and certainly systems where there are more than 12 pitches per octave. What I am hoping for is a term that describes and arbitrary instance of the ‘set of all notes that could be used in this musical context’.
Is it a ‘System’ or a ‘Musical Universe’ or some similar generalised term?
I would just call it a scale, like the scale of A minor, or with added qualifiers: the scale of A minor just intoned, etc. I like to associate scale with a musical ladder, and each note of the scale is represented by a rung of this ladder, representing a frequency pitch, exact or approximately. OTOH a mode is an interval pattern. By defining a base note we can construct a scale (ladder), which we can dance on musically.
PS: “musical scale” = “Tonleiter” in German, i.e ladder of tones.
That would be the origin of my association, having grown up in Germany.
Ah, but it is qualitatively different from a scale such as C Major. It is the palette of tones from which C Major is drawn. For a given musicality(?) it is the complete set of notes available for creating scales such as C Major.
Or to put it another way (and I apologize if my explanations are unclear): ‘Scale’ used to describe C Major is different to ‘Scale’ used to describe ‘set of all notes that could be used in this musical context’. The former is a subset of the latter. The ‘set of all notes that could be used in this musical context’ contains the notes in both to C Major and C# Major. And in a given musical context only the notes in this ‘set of all notes that could be used in this musical context’ can be used. Now musicians may treat these as different things with the same name, but in programming it may be better to use a different term. I was hoping to uncover that different term.
I want to give the program user the option to load another ‘set of all notes that could be used in a musical context’, but that is a bit wordy… Why give the user the option? Well, perhaps s/he wants to use a just-tempered set of notes. Or some ‘foreign’ (I hope that does not sound xenophobic) scheme that has different note names, or different base frequency (A=450), or different number of tones per octave… its easy to program, but hard for me to describe.
Do you mean all notes of the piano keyboard? Like all twelve semi tones of 12TET throughout a number of octaves, i.e. “twelve-tone chromatic”? But note there is no “just intoned” equivalent, there is no set of which just intoned scales are subsets. Any just intoned scale is mode specific.
Yes, indeed. All notes of a piano keyboard (and I suppose those on an unimaginably large piano too). I called the class in my program a ‘Chromatic’ - but that was just a guess at a pithy term that might be appropriate.
If we can go with the term ‘Chromatic’ for now (though I am still open to suggestions), then I would be giving the user a chance to choose a different Chromatic. The user will have to define the Chromatic (in a file in a rigid format). The user would load it into TWJCalc, choose a Scale Pattern (built in or of their choice) and a base note [and some other things such as tube ID, thickness…], and get the holes calculated for a whistle.
OK, I may have tripped over my own ignorance here. Do I understand that, given a just intoned ‘Chromatic’ containing the notes N1,N2,N3,N4…Nx you would only ever want a whistle with the notes N1,N2,N3,N4,N5,N6? That would still be possible under my proposed scheme, just not as neat a fit. The user would define the ‘Chromatic’, load it, specify N1 as base note, define and load a scale pattern of 1,1,1,1,1,1. And ‘Robert the long distance truck driver is your mothers long distance lover’.**
The ability to load a different ‘Chromatic’ is the only part of the prototype that I have not implemented yet…
** a modern day equivalent of the English colloquialism ‘Bobs your uncle’
Yep, but if they want to make a whistle in a ‘Chromatic’ other than 12TET A440 they have got to know what they are doing…
I do not know how much use such a facility will be, but I have learnt to avoid hard-coded data in a program. Someone will always think of a need for different data…
… although that might mean I need to allow for the speed of sound on both Jupiter and Mercury
Let me see if I can understand what you are asking. If so, I might have some useful responses. I think you are saying:
There is a set of notes such that they form the equal tempered 12 note scale based upon A=440 and from this set can be drawn subsets that correspond to various other scales using equal temperament which can be based on any note in the original set.
If that is what you mean then the answer is yes there are other sets of notes. The musicians would call them “temperaments” usually. However, they differ from the equal tempered set in that they are starting note specific. That is to say a 1/4 comma meantone set based on D would contain an F# but the pitch of that F# would not necessarily match the F# found in a 1/4 comman meantone set based on some other starting note. So, you could have subsets of, say, 8 or fewer notes, but you could not pick any note in the original set and create a subset based on it. Rather you would have to decide on your starting note (D for a common whistle?) and base the remaining notes on the pitch chosen for the starting D.
I’d suggest a look at “Tunings and Temperament” by Jan Murray Barbour (I think that is the correct spelling) and actually the discussions on Wikipedia of tuning and temperament are somewhat useful too.
So the term I was seeking was temperament? So when using a musical instrument calculator you would understand what was meant if you saw the term ‘load another temperament’?. If so then that is more satisfactory to me than calling it a ‘chromatic’ as at present.
As far as the actual use of a ‘1/4 comma meantone set based on D’, I understand (shallowly) why that is of use only for D based whistles. TWJCalc would still let you use such - though you would not need to define many notes. Out of interest, would you still wish to use different scale patterns (2 2 1 2 2 1), or is only one applicable? Either way TWJCalc can cope - you just might have to load a different scale pattern.
Actually, you could, in a slightly unobvious way, define any set of frequencies for your whistle. Just define a chromatic (sorry temperament) with just the notes that you want (name/frequency) and a scale pattern of 1 1 1 1 1 1 or 1 1 1 1 1 1 1 (TWJCalc copes with more or fewer than 6 tone holes).
As far as further reading goes, I have tried some of the recommendations, but, while it is fun, I find it hard to relate to the practical problems of writing the software. I wrote TWJCalc to satisfy my curiosity - I wanted to see the holes move as I changed their sizes. Everything after that has been added to make the tool more useful to the whistle-making public.
As you can tell by my profound ignorance of other chromatics/temperaments I have no use for them in my own whistle making, but adding the feature to the program was so easy that it seemed a shame not to do it. In doing it however, it makes sense to use the best (most commonly used) terminology.
The term Temperament does seem more appropriate, though, so for that (and the suggested reading) I am most grateful.
I don’t think “temperament” is the right term. Temperament is base-note specific, as is just intonation, as I already said. You can’t have an overall set of notes of a specific temperament, from which you then could select subsets of this temperament specific to individual base notes. The same is true for just intoned scales. Only chromatic scales divide an octave evenly in a logarithmic manner and let you have subsets of notes specific to musical modes.
Also bear in mind that just intonation does not result in a tempered scale. And that there are various just intoned scales, not just depending on the base note chosen, but also on the just intoned intervals chosen.
A user could define any of these scale patterns in separate files, like the program Scala does (see http://en.wikipedia.org/wiki/Scala_(program)). And then let the user define the base/root note of the scale and an exact reference pitch from within the GUI.
Like: Major scale in 12 tone equal tempered (12TET), base note D, pitch A=440Hz.
Or: Dorian just intoned, base note E, pitch A=435Hz.
Personally I find it sufficient to be able to select between just intonation (JI) (of a certain pattern of ratios) and equal temperament (12TET) for whistle construction.
I use this JI frequency ratio pattern for the standard major scale:
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1;
plus 16/9 for the minor seventh thumb hole (C nat on D whistle)
Gosh, it’s hard to get one’s head round these things at times. That is, of course, absolutely right, Hans. And yet, because any of the 50 or more JI scales or the hundreds and hundreds of tempered scales will provide all twelve tones within a given octave span, it’s really hard to get to grips with. But the convention, for theoretical purposes, is to base tempered scales and JI scales on C. Could we do that and produce a whole load of “chromatics” for Phill’s program? (Or, arbitrarily, base it on D instead, if we wanted.)
And, having got that far, I now realise that, in effect, that’s exactly what you’ve just discussed, Hans. Probably better than I’ve put it. Ho hum.
