User:Godtone: Difference between revisions

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I also think that powers of 2 in the denominator of an interval, broadly/generally speaking, helps the interval feel less disorienting due to a stronger suggestion of the fundamental, so beyond 13/12, for a bit, the superparticulars of the form (2n+1)/(2n) should be prioritised. This concludes at the following superparticular intervals being of particular (no pun intended) importance to a 'general melodic semi-harmonic system':

2/1, 3/2, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8, 10/9, 11/10, 12/11, 13/12, 15/14, 17/16, 19/18.

I stopped at 19/18 because (19/18)/(21/20) = 380/378 = 190/189 which is again under 11 cents. Note that this also corresponds to the 19-odd-limit, a subset of the 19-prime-limit, with 169/168 and 190/189 tempered. From there, we can choose to temper the missing superparticulars (the ones with odd denominators) to any of the adjacent superparticulars. Note that I am considering all of these intervals as intervals to move upwards with; 16/15 is an interval that to me works better for going downwards as it implies 15/8 = (3/2)(5/4) when you measure it relative to an imagined octave below the initial tone, and notice that 15/8 is expressible in terms of simple existing superparticulars (and thus as is 16/15). Also note that this does not mean I think the 19-limit should be where we stop. I think if we apply the idea of prime limit to Just Intonation music, the 23-limit is a far better stopping point due to being just before a record prime gap, and as there are various intervals using the prime 23 and more generally using the 27-odd-limit that I like.

I stopped at 19/18 because (19/18)/(21/20) = 380/378 = 190/189 which is again under 11 cents, as well as because superparticulars beyond 19/18 aren't really ''musically/melodically'' interesting to me. Note that this also corresponds to the 19-odd-limit, a subset of the 19-prime-limit, with 169/168 and 190/189 tempered. From there, we can choose to temper the missing superparticulars (the ones with odd denominators) to any of the adjacent superparticulars. Note that I am considering all of these intervals as intervals to move upwards with; 16/15 is an interval that to me works better for going downwards as it implies 15/8 = (3/2)(5/4) when you measure it relative to an imagined octave below the initial tone, and notice that 15/8 is expressible in terms of simple existing superparticulars (and thus as is 16/15). Also note that this does not mean I think the 19-limit should be where we stop. I think if we apply the idea of prime limit to Just Intonation music, the 23-limit is a far better stopping point due to being just before a record prime gap, and as there are various intervals using the prime 23 and more generally using the 27-odd-limit that I like.

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# minor, major (2 types)

# minor, neutral, major (3 types)

# (ultraminor or) ~~superminor~~, (supra)minor, (sub)major, supermajor (or ultramajor) (4 types)

# (ultraminor or) subminor, (supra)minor, (sub)major, supermajor (or ultramajor) (4 types)

# (ultraminor or) ~~superminor~~, minor, neutral, major, supermajor (or ultramajor) (5 types)

# (ultraminor or) subminor, minor, neutral, major, supermajor (or ultramajor) (5 types)

# (ultraminor,) ~~superminor~~, novaminor/neominor, minor, neutral, major, novamajor/neomajor, supermajor(, ultramajor) (7 (or 9) types)

# (ultraminor,) subminor, novaminor/neominor, minor, neutral, major, novamajor/neomajor, supermajor(, ultramajor) (7 (or 9) types)

# [same as 7 (or 9) types but with neutral split into subneutral & superneutral] (8 (or 10) types)

# [same as 8 (or 10) types but with either neo- & nova- distinguished (+2) or with supraminor & submajor added (+2)] (10 (or 12) types)

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Firstly, this will obviously be heavily influenced by ''my opinions'', so I may state subjective things or theories in a rather matter-of-fact way, but feel free to disagree with me/provide criticisms on my user page. Having said that... I think while measuring intervals relative to 12 EDO is useful initially, this should not be the final way of measuring them. Instead, I believe different intervals should be considered like "colours" or "flavours", of which 12 EDO's intervals are (approximately) one type (corresponding generally to novaminor and novamajor), and that these new terms (or whatever terms you prefer) should eventually be more natural a musical language than comparison to 12 EDO, which often causes a variety of intervals to be used similarly rather than distinguishing them as unique categories not subservient to (but related to) other categories. This is primarily due to a stark lack of theory in the ''musical'' and especially ''emotional'' meanings of these new intervals. This also makes me more open to the idea of using larger EDOs - which provide more distinctions - as frameworks in which many colours are possible, however, I have relatively high standards for large EDOs, as a large number of tones is something that needs to be quite seriously justified. For example, I generally dislike prime or not-very-composite EDOs unless they have exceedingly pure intervals and/or are very remarkable for other reasons. Sub-EDOs or extremely pure intervals in an EDO generally help to give it a feeling of griddedness and thus orientation in. I think the most important takeaway from 12 EDO is the effectiveness of simplicity and that you shouldn't underestimate how much can be built and how much nuance can be achieved by carefully combining simple things, and that the most objective possible interpretations of music come from the aggregation and combination of many patterns. This also leads me to believe scales are interpreted in terms of their pieces more than vice versa, as aforementioned.

Secondly, I think in new and unfamiliar territory, it will be helpful to use symbolism and analogies in order to get a rough initial understanding for potential emotional/symbolic meanings as the usual music theory isn't enough.

=== Number symbolism ===

'''1''' : Unity, simplicity & wholeness (obviously). The ultimate source/root. The Formless. The first Form.

'''2''' : Duality (obviously), contrast, distinction; the first prime number, and thus the first pure essence (assuming we don't count 1 as a pure essence). The source of the most basic/primitive/trivial kinds of order.

'''3''' : Trinity (obviously) and stability - due to each element helping define and stabilise the other two in relation to each-other; think of how the triangle is the strongest shape for scaffolding. Thus represents a place of completeness and strength, and sometimes, rest. (It is a pure essence due to being prime.)

'''4''' : The tetrahedron (AKA 3-simplex) has 4 vertices/corners, 4 sides/faces and 6 edges/connections with 3 edges/connections per vertex/corner. Thus represents the 3 spatial dimensions or the 3 dimensions of space paired with 1 dimension of time. The tetrahedron is a strong shape due to being made of 4 triangles, thus 4 similarly represents a place of completeness, strength and sometimes rest, but can be spiky/hazardous partly due to containing repeated duality (this applies (at least to small extent) to all numbers with powers of 2 in their prime factorisations) and thus pitfalls/negations of the ideal (as duality creates negation). Thus represents the Earth/its likeness (AKA the material world).

'''5''' : The number of sides of a square-based pyramid, which has 4 triangular sides and thus similar stability. 6 square based pyramids form a cube which tiles 3D space, and where squares themselves tile 2D space. Additionally, pentagons are the last 2D regular convex polygon for which you can join 3 to each-other and get something 3D, and thus 5 is also related to the dodecahedron, and thus the number 12. Also the 4 points of a tetrahedron with an added/unifying centre, thus representing Earthly dualities that have had their pitfalls tempered through unification through an ideal, or alternatively a triangle-based pyramid with its highest corner projected onto the ground, thus again representing construction upwards to something better, using what is available . Thus represents the pure essence of The Transcendent's grace on the Earth, AKA the first/simplest form of transcendence from/beyond the Earth (as it is 4+1). (It is a pure essence due to being prime.)

@@ Line 6: / Line 6: @@
 I also think that powers of 2 in the denominator of an interval, broadly/generally speaking, helps the interval feel less disorienting due to a stronger suggestion of the fundamental, so beyond 13/12, for a bit, the superparticulars of the form (2n+1)/(2n) should be prioritised. This concludes at the following superparticular intervals being of particular (no pun intended) importance to a 'general melodic semi-harmonic system':<br/>
 /1, 3/2, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8, 10/9, 11/10, 12/11, 13/12, 15/14, 17/16, 19/18.<br/>
-I stopped at 19/18 because (19/18)/(21/20) = 380/378 = 190/189 which is again under 11 cents. Note that this also corresponds to the 19-odd-limit, a subset of the 19-prime-limit, with 169/168 and 190/189 tempered. From there, we can choose to temper the missing superparticulars (the ones with odd denominators) to any of the adjacent superparticulars. Note that I am considering all of these intervals as intervals to move upwards with; 16/15 is an interval that to me works better for going downwards as it implies 15/8 = (3/2)(5/4) when you measure it relative to an imagined octave below the initial tone, and notice that 15/8 is expressible in terms of simple existing superparticulars (and thus as is 16/15). Also note that this does not mean I think the 19-limit should be where we stop. I think if we apply the idea of prime limit to Just Intonation music, the 23-limit is a far better stopping point due to being just before a record prime gap, and as there are various intervals using the prime 23 and more generally using the 27-odd-limit that I like.
+I stopped at 19/18 because (19/18)/(21/20) = 380/378 = 190/189 which is again under 11 cents, as well as because superparticulars beyond 19/18 aren't really ''musically/melodically'' interesting to me. Note that this also corresponds to the 19-odd-limit, a subset of the 19-prime-limit, with 169/168 and 190/189 tempered. From there, we can choose to temper the missing superparticulars (the ones with odd denominators) to any of the adjacent superparticulars. Note that I am considering all of these intervals as intervals to move upwards with; 16/15 is an interval that to me works better for going downwards as it implies 15/8 = (3/2)(5/4) when you measure it relative to an imagined octave below the initial tone, and notice that 15/8 is expressible in terms of simple existing superparticulars (and thus as is 16/15). Also note that this does not mean I think the 19-limit should be where we stop. I think if we apply the idea of prime limit to Just Intonation music, the 23-limit is a far better stopping point due to being just before a record prime gap, and as there are various intervals using the prime 23 and more generally using the 27-odd-limit that I like.
 <br/>
@@ Line 37: / Line 37: @@
 # minor, major (2 types)
 # minor, neutral, major (3 types)
-# (ultraminor or) superminor, (supra)minor, (sub)major, supermajor (or ultramajor) (4 types)
+# (ultraminor or) subminor, (supra)minor, (sub)major, supermajor (or ultramajor) (4 types)
-# (ultraminor or) superminor, minor, neutral, major, supermajor (or ultramajor) (5 types)
+# (ultraminor or) subminor, minor, neutral, major, supermajor (or ultramajor) (5 types)
-# (ultraminor,) superminor, novaminor/neominor, minor, neutral, major, novamajor/neomajor, supermajor(, ultramajor) (7 (or 9) types)
+# (ultraminor,) subminor, novaminor/neominor, minor, neutral, major, novamajor/neomajor, supermajor(, ultramajor) (7 (or 9) types)
 # [same as 7 (or 9) types but with neutral split into subneutral & superneutral] (8 (or 10) types)
 # [same as 8 (or 10) types but with either neo- & nova- distinguished (+2) or with supraminor & submajor added (+2)] (10 (or 12) types)
@@ Line 70: / Line 70: @@
 Firstly, this will obviously be heavily influenced by ''my opinions'', so I may state subjective things or theories in a rather matter-of-fact way, but feel free to disagree with me/provide criticisms on my user page. Having said that... I think while measuring intervals relative to 12 EDO is useful initially, this should not be the final way of measuring them. Instead, I believe different intervals should be considered like "colours" or "flavours", of which 12 EDO's intervals are (approximately) one type (corresponding generally to novaminor and novamajor), and that these new terms (or whatever terms you prefer) should eventually be more natural a musical language than comparison to 12 EDO, which often causes a variety of intervals to be used similarly rather than distinguishing them as unique categories not subservient to (but related to) other categories. This is primarily due to a stark lack of theory in the ''musical'' and especially ''emotional'' meanings of these new intervals. This also makes me more open to the idea of using larger EDOs - which provide more distinctions - as frameworks in which many colours are possible, however, I have relatively high standards for large EDOs, as a large number of tones is something that needs to be quite seriously justified. For example, I generally dislike prime or not-very-composite EDOs unless they have exceedingly pure intervals and/or are very remarkable for other reasons. Sub-EDOs or extremely pure intervals in an EDO generally help to give it a feeling of griddedness and thus orientation in. I think the most important takeaway from 12 EDO is the effectiveness of simplicity and that you shouldn't underestimate how much can be built and how much nuance can be achieved by carefully combining simple things, and that the most objective possible interpretations of music come from the aggregation and combination of many patterns. This also leads me to believe scales are interpreted in terms of their pieces more than vice versa, as aforementioned.<br/>
 Secondly, I think in new and unfamiliar territory, it will be helpful to use symbolism and analogies in order to get a rough initial understanding for potential emotional/symbolic meanings as the usual music theory isn't enough.
+<br/>
+=== Number symbolism ===
+'''1''' : Unity, simplicity & wholeness (obviously). The ultimate source/root. The Formless. The first Form.
+<br/>
+'''2''' : Duality (obviously), contrast, distinction; the first prime number, and thus the first pure essence (assuming we don't count 1 as a pure essence). The source of the most basic/primitive/trivial kinds of order.
+<br/>
+'''3''' : Trinity (obviously) and stability - due to each element helping define and stabilise the other two in relation to each-other; think of how the triangle is the strongest shape for scaffolding. Thus represents a place of completeness and strength, and sometimes, rest. (It is a pure essence due to being prime.)
+<br/>
+'''4''' : The tetrahedron (AKA 3-simplex) has 4 vertices/corners, 4 sides/faces and 6 edges/connections with 3 edges/connections per vertex/corner. Thus represents the 3 spatial dimensions or the 3 dimensions of space paired with 1 dimension of time. The tetrahedron is a strong shape due to being made of 4 triangles, thus 4 similarly represents a place of completeness, strength and sometimes rest, but can be spiky/hazardous partly due to containing repeated duality (this applies (at least to small extent) to all numbers with powers of 2 in their prime factorisations) and thus pitfalls/negations of the ideal (as duality creates negation). Thus represents the Earth/its likeness (AKA the material world).
+<br/>
+'''5''' : The number of sides of a square-based pyramid, which has 4 triangular sides and thus similar stability. 6 square based pyramids form a cube which tiles 3D space, and where squares themselves tile 2D space. Additionally, pentagons are the last 2D regular convex polygon for which you can join 3 to each-other and get something 3D, and thus 5 is also related to the dodecahedron, and thus the number 12. Also the 4 points of a tetrahedron with an added/unifying centre, thus representing Earthly dualities that have had their pitfalls tempered through unification through an ideal, or alternatively a triangle-based pyramid with its highest corner projected onto the ground, thus again representing construction upwards to something better, using what is available . Thus represents the pure essence of The Transcendent's grace on the Earth, AKA the first/simplest form of transcendence from/beyond the Earth (as it is 4+1). (It is a pure essence due to being prime.)
 <br/>