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m The references to "Armodue" were somewhat vague and didn't credit Pierpaolo Beretta at all.
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=Hexadecaphonic Notation=
=Hexadecaphonic Notation=


16-EDO notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO.
16-EDO notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. The Armodue model uses a 4-line staff for 16-EDO.


Moment of Symmetry Scales like Mavila [7] (or "Inverse/Anti-Diatonic" which reverses step sizes of diatonic from LLsLLLs to ssLsssL in the heptatonic variation) can work as an alternative to the traditional diatonic scale, while maintaining conventional A-G #/b notation as described above. Alternatively, one can utilize the Mavila[9] MOS, for a sort of "hyper-diatonic" scale of 7 large steps and 2 small steps. [[Armodue_theory|Armodue notation]] of 16-EDO "Mavila-[9] Staff" does just this, and places the arrangement (222122221) on nine white "natural" keys of the 16-EDO keyboard. If the 9-note "Enneatonic" MOS is adopted as a notational basis for 16-EDO, then we need an entirely different set of interval classes than any of the heptatonic classes described above; perhaps it even makes sense to refer to Octaves as 2/1, "[[Decave|Decave]]".
Moment of Symmetry Scales like Mavila [7] (or "Inverse/Anti-Diatonic" which reverses step sizes of diatonic from LLsLLLs to ssLsssL in the heptatonic variation) can work as an alternative to the traditional diatonic scale, while maintaining conventional A-G #/b notation as described above. Alternatively, one can utilize the Mavila[9] MOS, for a sort of "hyper-diatonic" scale of 7 large steps and 2 small steps. [[Armodue_theory|Armodue notation]] of 16-EDO "Mavila-[9] Staff" does just this, and places the arrangement (222122221) on nine white "natural" keys of the 16-EDO keyboard. If the 9-note "Enneatonic" MOS is adopted as a notational basis for 16-EDO, then we need an entirely different set of interval classes than any of the heptatonic classes described above; perhaps it even makes sense to refer to Octaves as 2/1, "[[Decave|Decave]]".
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==Metallic Harmony in 16 EDO==
==Metallic Harmony in 16 EDO==


Because 16 edo doesn't approximate 3/2 well at all, triadic harmony based on heptatonic thirds isn't a great option for typical harmonic timbres.
Because 16edo doesn't approximate 3/2 well at all, triadic harmony based on heptatonic thirds isn't a great option for typical harmonic timbres.


However, triadic harmony can be based on on heptatonic sevenths (or seconds) rather than thirds. For instance, 16 edo approximates 7/4 well enough to use
However, triadic harmony can be based on on heptatonic sevenths (or seconds) rather than thirds. For instance, 16edo approximates 7/4 well enough to use


it in place of the usual 3/2, and in Mavila[7] this 7/4 approximation shares an interval class with a well-approximated 11/6 (at 1050 cents). Stacking these two intervals reaches 2025¢, or a minor 6th plus an octave. Thus the out-of-tune 675¢ interval is bypassed, and all the dyads in the triad are consonant.
it in place of the usual 3/2, and in Mavila[7] this 7/4 approximation shares an interval class with a well-approximated 11/6 (at 1050 cents). Stacking these two intervals reaches 2025¢, or a minor 6th plus an octave. Thus the out-of-tune 675¢ interval is bypassed, and all the dyads in the triad are consonant.
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|-
|-
| style="text-align:center;" | 135/128
| style="text-align:center;" | 135/128
| | | -7 3 1 >
| |<nowiki> | -7 3 1 </nowiki>&gt;
| style="text-align:right;" | 92.18
| style="text-align:right;" | 92.18
| style="text-align:center;" | Major Chroma
| style="text-align:center;" | Major Chroma
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|-
|-
| style="text-align:center;" | 648/625
| style="text-align:center;" | 648/625
| | | 3 4 -4 &gt;
| |<nowiki> | 3 4 -4 </nowiki>&gt;
| style="text-align:right;" | 62.57
| style="text-align:right;" | 62.57
| style="text-align:center;" | Major Diesis
| style="text-align:center;" | Major Diesis
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|-
|-
| style="text-align:center;" | 3125/3072
| style="text-align:center;" | 3125/3072
| | | -10 -1 5 &gt;
| |<nowiki> | -10 -1 5 </nowiki>&gt;
| style="text-align:right;" | 29.61
| style="text-align:right;" | 29.61
| style="text-align:center;" | Small Diesis
| style="text-align:center;" | Small Diesis
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|-
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| | | 23 6 -14 &gt;
| |<nowiki> | 23 6 -14 </nowiki>&gt;
| style="text-align:right;" | 3.34
| style="text-align:right;" | 3.34
| style="text-align:center;" | Vishnuzma
| style="text-align:center;" | Vishnuzma
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|-
|-
| style="text-align:center;" | 36/35
| style="text-align:center;" | 36/35
| | | 2 2 -1 -1 &gt;
| |<nowiki> | 2 2 -1 -1 </nowiki>&gt;
| style="text-align:right;" | 48.77
| style="text-align:right;" | 48.77
| style="text-align:center;" | Septimal Quarter Tone
| style="text-align:center;" | Septimal Quarter Tone
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|-
|-
| style="text-align:center;" | 525/512
| style="text-align:center;" | 525/512
| | | -9 1 2 1 &gt;
| |<nowiki> | -9 1 2 1 </nowiki>&gt;
| style="text-align:right;" | 43.41
| style="text-align:right;" | 43.41
| style="text-align:center;" | Avicennma
| style="text-align:center;" | Avicennma
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|-
|-
| style="text-align:center;" | 50/49
| style="text-align:center;" | 50/49
| | | 1 0 2 -2 &gt;
| |<nowiki> | 1 0 2 -2 </nowiki>&gt;
| style="text-align:right;" | 34.98
| style="text-align:right;" | 34.98
| style="text-align:center;" | Tritonic Diesis
| style="text-align:center;" | Tritonic Diesis
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|-
|-
| style="text-align:center;" | 64827/64000
| style="text-align:center;" | 64827/64000
| | | -9 3 -3 4 &gt;
| |<nowiki> | -9 3 -3 4 </nowiki>&gt;
| style="text-align:right;" | 22.23
| style="text-align:right;" | 22.23
| style="text-align:center;" | Squalentine
| style="text-align:center;" | Squalentine
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|-
|-
| style="text-align:center;" | 3125/3087
| style="text-align:center;" | 3125/3087
| | | 0 -2 5 -3 &gt;
| |<nowiki> | 0 -2 5 -3 </nowiki>&gt;
| style="text-align:right;" | 21.18
| style="text-align:right;" | 21.18
| style="text-align:center;" | Gariboh
| style="text-align:center;" | Gariboh
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|-
|-
| style="text-align:center;" | 126/125
| style="text-align:center;" | 126/125
| | | 1 2 -3 1 &gt;
| |<nowiki> | 1 2 -3 1 </nowiki>&gt;
| style="text-align:right;" | 13.79
| style="text-align:right;" | 13.79
| style="text-align:center;" | Septimal Semicomma
| style="text-align:center;" | Septimal Semicomma
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|-
|-
| style="text-align:center;" | 1029/1024
| style="text-align:center;" | 1029/1024
| | | -10 1 0 3 &gt;
| |<nowiki> | -10 1 0 3 </nowiki>&gt;
| style="text-align:right;" | 8.43
| style="text-align:right;" | 8.43
| style="text-align:center;" | Gamelisma
| style="text-align:center;" | Gamelisma
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|-
|-
| style="text-align:center;" | 6144/6125
| style="text-align:center;" | 6144/6125
| | | 11 1 -3 -2 &gt;
| |<nowiki> | 11 1 -3 -2 </nowiki>&gt;
| style="text-align:right;" | 5.36
| style="text-align:right;" | 5.36
| style="text-align:center;" | Porwell
| style="text-align:center;" | Porwell
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|-
|-
| style="text-align:center;" | 121/120
| style="text-align:center;" | 121/120
| | | -3 -1 -1 0 2 &gt;
| |<nowiki> | -3 -1 -1 0 2 </nowiki>&gt;
| style="text-align:right;" | 14.37
| style="text-align:right;" | 14.37
| style="text-align:center;" | Biyatisma
| style="text-align:center;" | Biyatisma
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|-
|-
| style="text-align:center;" | 176/175
| style="text-align:center;" | 176/175
| | | 4 0 -2 -1 1 &gt;
| |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| style="text-align:right;" | 9.86
| style="text-align:right;" | 9.86
| style="text-align:center;" | Valinorsma
| style="text-align:center;" | Valinorsma
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|-
|-
| style="text-align:center;" | 385/384
| style="text-align:center;" | 385/384
| | | -7 -1 1 1 1 &gt;
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| style="text-align:right;" | 4.50
| style="text-align:right;" | 4.50
| style="text-align:center;" | Keenanisma
| style="text-align:center;" | Keenanisma
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|-
|-
| style="text-align:center;" | 441/440
| style="text-align:center;" | 441/440
| | | -3 2 -1 2 -1 &gt;
| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| style="text-align:right;" | 3.93
| style="text-align:right;" | 3.93
| style="text-align:center;" | Werckisma
| style="text-align:center;" | Werckisma
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|-
|-
| style="text-align:center;" | 3025/3024
| style="text-align:center;" | 3025/3024
| | | -4 -3 2 -1 2 &gt;
| |<nowiki> | -4 -3 2 -1 2 </nowiki>&gt;
| style="text-align:right;" | 0.57
| style="text-align:right;" | 0.57
| style="text-align:center;" | Lehmerisma
| style="text-align:center;" | Lehmerisma
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='''Armodue Theory (4-line staff)'''=
='''Armodue Theory (4-line staff)'''=
[http://www.armodue.com/ricerche.htm Armodue]: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions.
[http://www.armodue.com/ricerche.htm Armodue]: Pierpaolo Beretta's website for his "Armodue" theory for 16edo (esadekaphonic), including compositions.


Translations of parts of the Armodue pages can be found [[Armodue|here]] on this wiki.
Translations of parts of the Armodue pages can be found [[Armodue|here]] on this wiki.
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[http://www.cdbaby.com/cd/aeternamusic Tribute to Armodue] by Aeterna
[http://www.cdbaby.com/cd/aeternamusic Tribute to Armodue] by Aeterna


[http://www.io.com/%7Ehmiller/midi/16tet.mid Etude in 16-tone equal tuning] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/16tet.mp3 play] ([http://soonlabel.com/xenharmonic/archives/2604 organ version]) by [[Herman_Miller|Herman Miller ]]
[http://www.io.com/%7Ehmiller/midi/16tet.mid Etude in 16-tone equal tuning] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/16tet.mp3 play] ([http://soonlabel.com/xenharmonic/archives/2604 organ version]) by [[Herman_Miller|Herman Miller]]


[https://soundcloud.com/ron-sword/mavila-fog The Foggy Road from Pasadena] by Ron Sword
[https://soundcloud.com/ron-sword/mavila-fog The Foggy Road from Pasadena] by Ron Sword
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[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/05%20-%205.%2016%20octave.mp3 Comets Over Flatland 5] by [[Randy_Winchester|Randy Winchester]]
[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/05%20-%205.%2016%20octave.mp3 Comets Over Flatland 5] by [[Randy_Winchester|Randy Winchester]]


[http://micro.soonlabel.com/16-ET/20120527-16-malathion.mp3 Malathion] by [http://chrisvaisvil.com/?p=2358#comments Chris Vaisvil ]
[http://micro.soonlabel.com/16-ET/20120527-16-malathion.mp3 Malathion] by [http://chrisvaisvil.com/?p=2358#comments Chris Vaisvil]


[http://micro.soonlabel.com/16-ET/20130216_16edo_vesta.mp3 Being of Vesta] by [http://chrisvaisvil.com/?p=3061 Chris Vaisvil]
[http://micro.soonlabel.com/16-ET/20130216_16edo_vesta.mp3 Being of Vesta] by [http://chrisvaisvil.com/?p=3061 Chris Vaisvil]
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<span style="display: block; height: 1px; left: 0px; overflow: hidden; position: absolute; top: 3102px; width: 1px;"><span style="font-family: Palatino; font-size: medium;">[http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-19%2C7%2C1%3E&limit=2_5_7 546875:524288]</span>
<span style="display: block; height: 1px; left: 0px; overflow: hidden; position: absolute; top: 3102px; width: 1px;"><span style="font-family: Palatino; font-size: medium;">[http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-19%2C7%2C1%3E&limit=2_5_7 546875:524288]</span>
</span>


[[Category:16-tone]]
[[Category:16-tone]]
Retrieved from "https://en.xen.wiki/w/16edo"