Hello Tuning World

Hi all. I thought I'd post a message with more details about myself as a way of saying "Hello" to the group.

I am a professional trumpet player and come to this group primarily from the perspective of performance. I have been playing with just intonation for several years, starting when I began trying to explain tuning during trumpet sectionals in college. I even started a web site for this purpose, based partly on my master's thesis "The Effect of Valves on the Intonation of the B-flat Trumpet." The site's not finished yet (will it ever be?), but here's the URL:

http://www.csulb.edu/~mullen

The "Musicians Intonation Site" (I wanted to call it the "Players Intonation Site", but didn't think the acronym was, ah, suitable) is essentially a place where I refer players to whom I am attempting to introduce the concept of real tuning, as opposed to the absolute pitch-matching that is taught in schools. I hate it when I see other instrumentalists blowing into an electronic tuner while playing a major third or dominant seventh. Aaugh!

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Ever since I discovered the pitch drift inherent in a strict adherance to just tuning I've been playing with converting short pieces to just tuning for the purpose of exploring that phenomenon. I have been exploring it for a few years, as time permits, but without much knowledge of what others were doing in this area. (I recently made acquaintance with John deLaubenfels after finding his adaptive tuning work on his web site. He steered me to this group.)

I used to do my tuning experiments on synthesizers (Roland SC-55 & Korg 05R/W), but became dissolusioned with the time taken to enter all the pitch bends and with the ever-present sample loops that ruin the smoothness of just intervals.

Then I discovered Csound! Now I use an Excel workbook with several interlinking spreadsheets for my adaptive tuning work. In a nutshell, one sheet holds an imported MIDI file that has been converted to text. This sheet also provides a convenient place to specify key and transposition, if needed. Another sheet supplies tables of pitch class and equally tempered frequencies for the MIDI note numbers, and a third sheet supplies the ratios associated with the diatonic major and minor scales. These include only dominant-side ii (9/8) and vii (9/5). I haven't automated contextual tuning yet, so I have to hand-tune plagal-side ii (10/9) and vii (16/9) and dominant 7ths. The diatonic chords are mostly 5-limit, but dominant 7ths are 7-limit. Finally, yet another sheet is used as an export platform to Csound.

An aside: If I understand Partch correctly, my term "dominant-side" would be his otonal, while "plagal-side" (subdominant) would be utonal. Though Partch's mathematics are cool, his harmonies and concepts exist in a context outside of the compass of the instruments I play and work with, so I haven't picked up his terminology. Mr. Practical here!

Anyway, I am currently hacking away at the Gabrieli Sonata pian' e forte, my work on which is specifically geared toward exploring tuning drift. I have modified my spreadsheet to allow me to insert commas as needed without the need to change the ratios used on individual notes. Otherwise the ratios would quickly become unrecognizable, as you can imagine.

The Gabrieli supplies some interesting quirks. For example, there is often one note held over a chord change, and the chord sequences sometimes take off on a sojourn through several secondary dominant relationships in just a few bars. This combination of held notes and constant modulation can quickly flatten the pitch by a comma or more. If this effect were the only one, the pitch would drop by just over 150 cents by the end of the piece (81 bars). Most of the flattening takes place in two relatively short passages, though.

But wait! There's more! There are several D's (I put the piece in A-minor for convenience) that start out as the root of IV but are held across a bar line to become the dom7 of V7. When playing such a note on my trumpet I will, as subtly as possible, flatten the D to suit it's new role. But the whole point of this excercise is to brutally follow wherever the pitch takes me, so in these instances I must RAISE the non-held pitches by 64/63 so the D-4/3 is a relative 7/4 to the E! Yeehaw! The net result may well mean an overall sharpening of pitch throughout the piece, but it's a wash so far. I'll post more when I get it done...

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Patrick K. Mullen |
California State University, Long Beach | .___TTT____/
http://www.csulb.edu/~mullen | (_u|||o_) \
(562) 985-7937 |
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