The authors of this article met on a Master of Arts (MA) music education course a month before the Swanwick Tillman Sequence of Musical Development was published. The course was a portal to an exciting range of literature, with the Swanwick Tillman spiral providing a long-term source of discussion and reflection as our careers have diverged and converged over the intervening years. This paper takes the form of a duoethnographic conversation in which we summarise and reflect on that ongoing synergistic discussion, showing the influence the spiral has had within our particular situations.

It can be argued that Swanwick’s research and scholarship established the field of music education as an area of interdisciplinary study in the United Kingdom. A significant and seminal publication in this legacy is Swanwick’s work with Tillman on the sequence of musical development based on Tillman’s empirical study of children’s compositions. This paper will aim to place the resulting ‘spiral’ in the wider context of Swanwick’s meta-theory of music education and to understand some of the critical issues surrounding it. The paper will conclude with an appraisal of Swanwick’s impact on the theory and practice of music education.

Swanwick and Tillman set out three levels at which their “Sequence of Musical Development” may implicate music teaching: general curriculum planning, individual development, and the role of the teacher. From the perspective of a practitioner working as a secondary music teacher in England, this article critiques the practicalities of adopting an approach inspired by Swanwick and Tillman’s theory. Although recognising the challenges that music teachers face in the current context for music education, this article argues that educators should carefully consider how musical learning is structured, both in curriculum planning and approach.

The notion of the spiral for progression and development is familiar both in general educational discourse and in the domain of music education. This brief article considers the spiral within the context of lower secondary school group composing in England. Through the use of examples taken from two schools in the English midlands, it argues that formative assessment is a key process for enhancing spiral-like musical learning.

The paper discusses the Garboldisham macehead: an unusual decorated macehead carved from red deer antler. The macehead was found in the 1960s deposited in a tributary of the river Little Ouse, Norfolk and is decorated with three spirals, making it especially significant. This paper reports on the analysis of the decoration using digital imaging, discusses a new radiocarbon date recently obtained for the artefact, and discusses its significance alongside other dated antler maceheads.

The warm ionised medium (WIM), also referred to as diffuse ionised gas (DIG), contains most of the mass of interstellar medium in ionised form, contributing as much as 30% of the total atomic gas mass in the solar neighborhood. The advent of CCDs has enabled unprecedented study of this medium in external galaxies, probing a variety of environments. In particular, we can derive the morphology of the WIM, its distribution across disks, and the correlation with other Population I material. Spectroscopy of the WIM makes it possible to test various ionisation models. I will review here our current understanding of the properties of the WIM in spiral galaxies. A perhaps unexpected result is that the Hα emission from the WIM contributes about 40% of the total observed Hα luminosity from spirals. This places severe constraints on possible sources of ionisation, since only photoionisation by OB stars meets this requirement. Spectroscopic measurements of forbidden line strengths appear in reasonable agreement with photoionisation models. It is not yet clear if the Lyman continuum photons that ionise the WIM are mostly from OB stars located inside traditional HII regions, or from field OB stars.

The J = 1–0 rotational transition of carbon monoxide has been used to trace the molecular gas at five different positions in the Circinus galaxy using the Australia Telescope National Facility's 22 m radio telescope at Mopra. The intensity profile of the central CO emission has a full width at half maximum of 550 pc. The 12CO (1–0) spectrum at the centre of the galaxy has an integrated temperature of 145 K km S−1, with components peaking at 0·62 K and ranging in velocity from 200–600 km S−1. The total mass of molecular gas in the Circinus galaxy, assuming that the CO intensity profile of the galaxy is similar to the radio continuum, is at least 7·5±4·1 × 108 M⊙. This estimate, combined with previously published far infrared data, yields a value for the star-forming efficiency, SFE = 16±9 L⊙ M⊙‒1.

The outskirts of galaxies — especially the very extended Hi disks of galaxies — are strongly affected by their local environment. I highlight the giant 2X-Hi disks of nearby galaxies (M 83, NGC 3621, and NGC 1512), studied as part of the Local Volume Hi Survey (LVHIS), their kinematics and relation to XUV disks, signatures of tidal interactions and accretion events, the MHI - DHI relation as well as the formation of tidal dwarf galaxies. - Using multi-wavelength data, I create 3D visualisations of the gas and stars in galaxies, with the shape of their warped disks obtained through kinematic modelling of their Hi velocity fields.

This paper explores the possibilities of very simple analysis on derivation of spiral regions for a single segment of cubic function matching positional, tangential, and curvature end conditions. Spirals are curves of monotone curvature with constant sign and have the potential advantage that the minimum and maximum curvature exists at their end points. Therefore, spirals are free from singularities, inflection points, and local curvature extrema. These properties make the study of spiral segments an interesting problem both in practical and aesthetic applications, like highway or railway designing or the path planning of non-holonomic mobile robots. Our main contribution is to simplify the procedure of existence methods while keeping it stable and providing flexile constraints for easy applications of spiral segments.

The corotation radius in a spiral galaxy is the place where the spiral pattern speed has the same velocity of the rotation curve. By compiling results coming from the literature for 20 spiral galaxies we verified a strong correlation between the radius of the minima or inflections of the metallicity distribution and the corotation radius.

The stellar mass-metallicity relations of star-forming galaxies at intermediate-z (0.4<z<1) and high-z (z≥2) are compared with the local SDSS galaxies. It shows obvious evolutionary effect, i.e., at a given stellar mass, the intermediate-z galaxies show about 0.3 dex lower metallicity, and the high-z galaxies show about 0.56 dex more metal-deficient than the local ones. These distant galaxies will produce these important parts of their metals during the consequent evolutionary process. A close-box model can explain this evolutionary process generally.

Using a large sample of ~40,000 star-forming galaxies selected from the SDSS, we derive oxygen abundance calibrations from strong-line ratios, such as [N II]/Hα, [O III]/[N II], [N II]/[O II], [N II]/[S II], [S II]/Hα, and [O III]/Hβ. The derived analytic calibrations cover a quite wide range of metallicity, from 12+log(O/H)= 7.1 to 9.3. These calibrations can be used as calibration references for the future studies about metallicities of star-forming galaxies.

NGC 5055 is one of a list of nearby large spiral galaxies we have selected for a morphological and kinematic study of their bulges. CCD images are obtained at various spectral bands and in the Hα line using the 2.1 m reflector at San Pedro Martir observatory in México, while long-slit spectra at four different PA's are secured with the IDS spectrograph of the Isaac Newton Telescope of the observatory Roque de los Muchachos at La Palma, Spain. Some of the galaxies on our list for which observations are already performed are, aside from NGC 5055, NGC 3351, 4314, 5383 and 5915. These galaxies are not known to have active nuclei. However, we believe that activity may be a common phenomenon spanning a wide range of energetics, from the most active quasars and radio-galaxies (with jets) down to the mildest cases like our Galaxy or M31. The latter may be designated as MAGN (mildly active galactic nuclei). These ideas are treated in a review by Pişmiş (1987, Rev. Mex. Astron. Astrof. 14). The MAGN are usually nearby, and hence offer the possibility to study them in sufficient detail. It is reasonable to expect that the physical phenomenon underlying activity in galactic nuclei is one and the same, and it is essentially the global parameters such as energy at the nucleus that give rise to the different classes of AGN. Thus by studying the nearby mildly active galaxies one can construct a physically acceptable model supported by observation; such model, based on firmer grounds, can then be applied to all AGN.

NGC 5055 (Sbc) with an adopted distance of 8.2 Mpc has a very bright bulge with a tenuous multiple arm structure around it, extending to 8 arcmin. Our velocity field and morphology of NGC 5055 lead to the following conclusions.

1. The galaxy presents a north-south asymmetry; the southern approaching side has its isophotes closer together than at the farther side. We adopt PA 101° for the line of nodes. Our long-slit spectra cover the position angles: 58°, 101°, 112° and 155°.

2. The rotation curve shows a linear region around the nucleus. At PA 101°, the line of nodes, the amplitude is 270 km s−1 between points ±5 arcsec on either side of the nucleus.

3. There is high concentration of mass at the nuclear region (the bulge of the galaxy). An estimate of the mass for the region where the rotation curve is linear ±5 arcsec, is 1.5 × 108 M⊙. Burbidge et al. (1960) give a total mass of 7.6 × 1010 M⊙. The bulge density is thus found to be 500 times the average density of this galaxy.

Analysis of the general velocity field based on four long-slit spectra shows an asymmetry between the East and West sides, ±5 arcsec around the nucleus of NGC 5055, suggestive of the existence of non-circular motion. Indeed evidence is found of an outflow on the west side of the Galaxy within a cone emanating from the center towards the NW with a projected radial velocity of around 80 km s−1. Thus this galaxy shows activity at its center and is a candidate for the MAGN group.