Topic: Meantune
1 scales
| File | Description | Notes | Period (¢) |
|---|---|---|---|
| meantune | Meantune scale/temperament | 16 | 1200.0 |
Thread (6 messages)
From: Gene Ward Smith (2003-06-18) Subject: Meantune Here is something which can be regarded as either a scale or a temperament, depending on your point of view. It has a lot of nice tunings and can play meantone music among its other talents. It would be a good one to try on a guitar, I think. It comes equipped with sixteen notes to the octave; it has a circle of five meantone fifths of various sizes (various since I did an rms optimaization), with the final "fifth" actually being an 11/9 neutral third. It thereby has fifteen fifths, between 6.2 and 4.2 cents flat, and an 11/9 1.3 cents sharp. Besides that, it has twelve major thirds, ranging from .17 cents flat to 1.0 cent sharp, thirteen minor thirds between 4.1 and 6.9 cents flat, seven subminor thirds between 2.97 and 4.0 cents sharp, six 7/4's between 1.8 and 1.2 cents flat, and a 3.6 cent flat 11/6. It also has twelve major and twelve minor meantone-related triads, allowing you to fake your way through all kinds of standard repertorie pieces, six major and minor tetrads, allowing you do to a lot more than that, and the aforementioned dash of 11-limit for flavoring. ! meantune.scl Meantune scale/temperament 16 ! 77.186671 116.099742 193.485158 309.606987 386.992404 425.905475 503.092146 580.123259 620.006163 695.751153 812.878174 890.213971 1007.340993 1083.085983 1122.968886 1200.00000
From: Gene Ward Smith (2003-06-18) Subject: Re: Meantune --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote: > It comes equipped with sixteen notes to the octave; it has a circle of > five meantone fifths ^^^^^^^ Fifteen! of various sizes (various since I did an rms > optimaization), with the final "fifth" actually being an 11/9 neutral > third. It thereby has fifteen fifths, between 6.2 and 4.2 cents flat, > and an 11/9 1.3 cents sharp. Besides that, it has twelve major thirds, > ranging from .17 cents flat to 1.0 cent sharp, thirteen minor thirds > between 4.1 and 6.9 cents flat, seven subminor thirds between 2.97 and > 4.0 cents sharp, six 7/4's between 1.8 and 1.2 cents flat, and a 3.6 > cent flat 11/6. It also has twelve major and twelve minor > meantone-related triads, allowing you to fake your way through all > kinds of standard repertorie pieces, six major and minor tetrads, > allowing you do to a lot more than that, and the aforementioned dash > of 11-limit for flavoring. > > ! meantune.scl > Meantune scale/temperament > 16 > ! > 77.186671 > 116.099742 > 193.485158 > 309.606987 > 386.992404 > 425.905475 > 503.092146 > 580.123259 > 620.006163 > 695.751153 > 812.878174 > 890.213971 > 1007.340993 > 1083.085983 > 1122.968886 > 1200.00000
From: Gene Ward Smith (2003-06-18) Subject: Re: Meantune --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote: > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote: > > > It comes equipped with sixteen notes to the octave; it has a circle of > > five meantone fifths > ^^^^^^^ > > Fifteen! Do any of the history experts here know if meantone16, with four split keys, was ever actually used? If so, might it have been tuned in 1/4 comma?
From: Kurt Bigler (2003-06-18) Subject: Re: [tuning] Re: Meantune on 6/17/03 7:54 PM, Gene Ward Smith <gwsmith@svpal.org> wrote: > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote: >> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote: >> >>> It comes equipped with sixteen notes to the octave; it has a circle of >>> five meantone fifths >> ^^^^^^^ >> >> Fifteen! > > Do any of the history experts here know if meantone16, with four split > keys, was ever actually used? If so, might it have been tuned in 1/4 > comma? Here is another excerpt from Padgham, The Well-Tempered Organ, 1986, from the section "Quarter Comma Mean Tone": ***** ***** ***** ***** ... extra split notes available on the new organ built in 1768 for the Foundling Hospital in London, by Thomas Parker which had four additional notes available in each octave. These were D#, Ab, Db, and A#, as well as Eb, G#, C#, and Bb already provided. It is interesting that a 17th c. type organ built in 1981 by Brombaugh in the Fairchild Chapel, Oberlin College, Ohio, U.S.A. is tuned to 1/4 comma mean tone and has three split keys on the Great giving D#/Eb, G#/Ab, and A#/Bb. (Kiraly, 1981, Porter 1981). Furthermore from Table 6 it can be seen that C# major and F# major cannot be made good keys by the additin of D# and Ab alone, so these are still unusable keys on a split key organ. The require for good intonation the additional notes E#, A#, Cb. These extra notes are also available on the McClure organ, and thus good intonation can be had in all the keys in mean tone tuning. ***** ***** ***** ***** The McClure organ was disccused in an earlier chapter "Why do we need keyboard temperament?" in some detail: ***** ***** ***** ***** One extant ingenious example is the McClure organ built by Harrison and Harrison of Durham (McClure 1951) (FIgure 5) which is now in the Department of Music of the University of Edinburgh. Dr A.R. McClure ... realised that the cathedral choirs and madrigal groups sang 16th and 17th century music unaccompanied because any accompanying instrument tuned in equal temperament sounded horrible. Unfortunately, Dr. McClure died before the organ was completed, but it was finished in 1950 under the sueprvision of Dom Laurence Bévenot and was first erected in Ampleforth Abbey. ... The organ is tuned to the 19 note scale of Robert Smith, a mid-18th c. Master of Trinity College, Cambridge. It has a normal keyboard with the usual five accidental (black) notes. There are, however, 19 pipes provided for each octave. The organ has seven extra key stops (Figure 6). When none of these is drawn the black keys sound the following pipes, C#, Eb, F#, G# and Bb. This enables one to play, say, in the key of A major. To play in the key of Eb major, the player draws the knob marked Ab. This causes the middle black keys to sound the Ab pipes, instead of the G# pipes. ***** ***** ***** ***** That section goes on to describe a 32-note/octave "Voice Harmonium made by Colin Brown in 1875" and a just intonation pipe organ built in 1981 by the Belgian organ builder Stephan Schumacher, based on principles "evolved by Professor Dr Martin Vogel of the University of Bonn (Vogel 1980), which has 48 pipes per octave. An electronic instrument with 171 notes per octave is also mentioned, somehow associated with the previous instrument. References for the above excerpts: Kiraly W. & P. 1981 "Summer Organ Institute Recital", the Diapason, Dec 1981, pp 17-18. Porter W. 1981 "The Meaning of Mean-Tone Temperament", The Diapason, Dec 1981, p 19 McClure A.R. 1951 "An extended mean-tone organ", The Organ, no 119, pp 139-141 Vogel M. 1980 Musiktheater I, Bonn -Kurt Bigler
From: wallyesterpaulrus (2003-06-18) Subject: Re: Meantune --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote: > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote: > > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote: > > > > > It comes equipped with sixteen notes to the octave; it has a circle of > > > five meantone fifths > > ^^^^^^^ > > > > Fifteen! > > Do any of the history experts here know if meantone16, with four split > keys, was ever actually used? If so, might it have been tuned in 1/4 > comma? helmholtz and other sources describe handel's organ this way, except that instead of split keys, stops were used to select which consecutive set of 11 fifths was used (in accordance with then-contemporary harpsichord retuning practice). thus handel would probably never have been able to play those neutral thirds. there are in inordinate number of posts on handel's organ to be found in the archives of this list.
From: Gene Ward Smith (2003-06-19) Subject: Re: Meantune --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote: > helmholtz and other sources describe handel's organ this way, except > that instead of split keys, stops were used to select which > consecutive set of 11 fifths was used (in accordance with > then-contemporary harpsichord retuning practice). thus handel would > probably never have been able to play those neutral thirds. It's too bad Handel or someone didn't experiment with it; it makes a nice set of tones considered as a scale in itself, and not just as something to do diatonic music with. Good for someone who wants to fool with 31-equal, certainly.